Beyond Moore’s technologies: operation principles

of a superconductor alternative

Uploaded:22.01.18

Modified:22.01.18

File Size:2 MB

Modified:22.01.18

File Size:2 MB

**Authors:**

Igor I. Soloviev, Nikolay V. Klenov, Sergey V. Bakurskiy, Mikhail Yu. Kupriyanov, Alexander L. Gudkov and Anatoli S. Sidorenko

The predictions of Moore's law are considered by experts to be valid until 2020 giving rise to "post-Moore's" technologies afterwards. Energy efficiency is one of the major challenges in high-performance computing that should be answered. Superconductor digital technology is a promising post-Moore's alternative for the development of supercomputers. In this paper, we consider operation principles of an energy-efficient superconductor logic and memory circuits with a short retrospective review of their evolution. We analyze their shortcomings in respect to computer circuits design. Possible ways of further research are outlined.

Bunching of numbers in a non-ideal roulette: the key to winning strategies

Uploaded:20.01.16

Modified:20.01.16

File Size: 2 MB

**Authors:** A. V. Kavokin, A. S. Sheremet and M. Yu. Petrov

Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a realistic roulette is not ideal: the probabilities of realisation of different numbers slightly deviate. Describing this deviation by a statistical distribution with a width δ we find a critical δ that equalizes chances of gambler and casino in the case of a simple strategy of the game: the gambler always puts equal bets to the last N numbers. For up-critical δ the expected return of the roulette becomes positive. We show that the dramatic increase of gambler's chances is a manifestation of bunching of numbers in a non-ideal roulette. We also estimate the critical starting capital needed to ensure the low risk game for an indefinite time.

Modified:20.01.16

File Size: 2 MB

Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, a realistic roulette is not ideal: the probabilities of realisation of different numbers slightly deviate. Describing this deviation by a statistical distribution with a width δ we find a critical δ that equalizes chances of gambler and casino in the case of a simple strategy of the game: the gambler always puts equal bets to the last N numbers. For up-critical δ the expected return of the roulette becomes positive. We show that the dramatic increase of gambler's chances is a manifestation of bunching of numbers in a non-ideal roulette. We also estimate the critical starting capital needed to ensure the low risk game for an indefinite time.

From local force-flux relationships to internal dissipations and their impact on heat engine performance: The illustrative case of a thermoelectric generator

Uploaded:04.09.13

Modified:04.09.13

File Size:269 KB

**Authors:** Y. Apertet, H. Ouerdane, C. Goupil and Ph. Lecoeur

We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager’s reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: The linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand and of two classes of heat engines, autonomous and periodically driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a “thermal” thermopower and an “electrical” thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.

Modified:04.09.13

File Size:269 KB

We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager’s reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: The linear behavior of a heat engine at the local scale is associated with a dissipation process that must partake in the global energy balance. We discuss the consequences of internal dissipations on the so-called efficiency at maximum power, in the light of our comparative analyses of exoreversibility and endoreversibility on the one hand and of two classes of heat engines, autonomous and periodically driven, on the other hand. Finally, basing our analysis on energy conservation, we also discuss recent works which claim the possibility to overcome the traditional boundaries on efficiency imposed by finite-time thermodynamics in thermoelectric systems with broken time-reversal symmetry; this we do by introducing a “thermal” thermopower and an “electrical” thermopower which permits an analysis of the thermoelectric response of the TEG considering a possible dissymmetry between the electrical/thermal and the thermal/electrical couplings.

On the efficiency at maximum cooling power

Uploaded:04.09.13

Modified:04.09.13

File Size:424 KB

**Authors:** Y. Apertet, H. Ouerdane, A. Michot, C. Goupil and Ph. Lecoeur

The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency ηCA being considered as a universal upper bound. Yet, no valid counterpart to ηCA has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators.

Modified:04.09.13

File Size:424 KB

The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency ηCA being considered as a universal upper bound. Yet, no valid counterpart to ηCA has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators.

Why the Expansion of the Universe Appears to Accelerate

Uploaded:17.06.13

Modified:17.06.13

File Size:685 KB

**Author:** Paul Smeulders

A Speed of Light falling over time inversely proportional to the expansion of the Universe leads to an experimentally observed exponential changing of the Red Shift over time. It is necessary to re-define the Angular Impulse Momentum in order to get a consistent expansion of space on all levels. Conservation of Energy and this newly defined Angular Impulse Momentum then leads to the requirement that all clocks slow down in time inversely proportional to the Red Shift, independent of whether the Speed of Light is constant or not. From the Lorentz equation it then follows that Ex- pansion occurs over space-time and not over space alone. A steady state expansion in true time is then transformed into an exponential expansion for an observer with a local clock. A finite lifetime of the Universe is transformed to an infi- nite lifetime for these observers including elementary particles.

Modified:17.06.13

File Size:685 KB

A Speed of Light falling over time inversely proportional to the expansion of the Universe leads to an experimentally observed exponential changing of the Red Shift over time. It is necessary to re-define the Angular Impulse Momentum in order to get a consistent expansion of space on all levels. Conservation of Energy and this newly defined Angular Impulse Momentum then leads to the requirement that all clocks slow down in time inversely proportional to the Red Shift, independent of whether the Speed of Light is constant or not. From the Lorentz equation it then follows that Ex- pansion occurs over space-time and not over space alone. A steady state expansion in true time is then transformed into an exponential expansion for an observer with a local clock. A finite lifetime of the Universe is transformed to an infi- nite lifetime for these observers including elementary particles.

Mesoscopic thermoelectric transport near zero transmission energies

Uploaded:22.04.13

Modified:22.04.13

File Size:913 KB

**Authors:** YA. Abbout, H. Ouerdane and C. Goupil

We study the thermoelectric transport coefficients of a one-dimensional (1D) electron waveguide connected to one and then two off-channel cavities, in the presence of dephasing phonons. The model system is that of a linear chain described as a 1Dlattice. For simplicitywe consider single-mode cavities, whichmay be tunedwith external gates. While the presence of only one off-channel cavity yields a nearly symmetric transmission profile, which is canceled around the cavity mode, an additional cavity modifies this profile strongly and results in an asymmetric shape characterized by oscillations. In both cases,we consider electron-phonon interactions in our calculations and analyze their effects on the transmission function around the Fermi energy. Knowledge of the energy-dependent transmission function allows the numerical computation of thermoelectric transport coefficients, including the thermopower. In the presence of a second off-channel cavity, the sign of the thermopower depends on the relative position of this cavity energy level with respect to the Fermi energy: the thermopower is positive when low-energy electrons in the vicinity of the Fermi level are not transmitted and becomes negative when the higher-energy electrons are not transmitted.

Modified:22.04.13

File Size:913 KB

We study the thermoelectric transport coefficients of a one-dimensional (1D) electron waveguide connected to one and then two off-channel cavities, in the presence of dephasing phonons. The model system is that of a linear chain described as a 1Dlattice. For simplicitywe consider single-mode cavities, whichmay be tunedwith external gates. While the presence of only one off-channel cavity yields a nearly symmetric transmission profile, which is canceled around the cavity mode, an additional cavity modifies this profile strongly and results in an asymmetric shape characterized by oscillations. In both cases,we consider electron-phonon interactions in our calculations and analyze their effects on the transmission function around the Fermi energy. Knowledge of the energy-dependent transmission function allows the numerical computation of thermoelectric transport coefficients, including the thermopower. In the presence of a second off-channel cavity, the sign of the thermopower depends on the relative position of this cavity energy level with respect to the Fermi energy: the thermopower is positive when low-energy electrons in the vicinity of the Fermi level are not transmitted and becomes negative when the higher-energy electrons are not transmitted.

Efficiency at maximum power of thermally coupled

heat engines

Uploaded:07.11.12

Modified:07.11.12

File Size:562 KB

**Authors:** Y. Apertet, H. Ouerdane, C. Goupil and Ph. Lecoeur

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique.We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focus on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: The EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We discuss our results in light of nonideal Carnot engine behavior.

vity energy level with respect to the Fermi energy: the thermopower is positive when low-energy electrons in the vicinity of the Fermi level are not transmitted and becomes negative when the higher-energy electrons are not transmitted.

Modified:07.11.12

File Size:562 KB

We study the efficiency at maximum power of two coupled heat engines, using thermoelectric generators (TEGs) as engines. Assuming that the heat and electric charge fluxes in the TEGs are strongly coupled, we simulate numerically the dependence of the behavior of the global system on the electrical load resistance of each generator in order to obtain the working condition that permits maximization of the output power. It turns out that this condition is not unique.We derive a simple analytic expression giving the relation between the electrical load resistance of each generator permitting output power maximization. We then focus on the efficiency at maximum power (EMP) of the whole system to demonstrate that the Curzon-Ahlborn efficiency may not always be recovered: The EMP varies with the specific working conditions of each generator but remains in the range predicted by irreversible thermodynamics theory. We discuss our results in light of nonideal Carnot engine behavior.

vity energy level with respect to the Fermi energy: the thermopower is positive when low-energy electrons in the vicinity of the Fermi level are not transmitted and becomes negative when the higher-energy electrons are not transmitted.

Irreversibilities and efficiency at maximum power of heat engines: The illustrative case of a thermoelectric generator

Uploaded:7.11.12

Modified:07.11.12

File Size:235 KB

**Authors:** Y. Apertet, H. Ouerdane, C. Goupil and Ph. Lecoeur

Energy conversion efficiency at maximum output power, which embodies the essential characteristics of heat engines, is the main focus of the present work. The so-called Curzon and Ahlborn efficiency ηCA is commonly believed to be an absolute reference for real heat engines; however, a different but general expression for the case of stochastic heat engines, ηSS, was recently found and then extended to low-dissipation engines. The discrepancy between ηCA and ηSS is here analyzed considering different irreversibility sources of heat engines, of both internal and external types. To this end, we choose a thermoelectric generator operating in the strong-coupling regime as a physical system to qualitatively and quantitatively study the impact of the nature of irreversibility on the efficiency at maximum output power. In the limit of pure external dissipation, we obtain ηCA, while ηSS corresponds to the case of pure internal dissipation. A continuous transition between from one extreme to the other, which may be operated by tuning the different sources of irreversibility, also is evidenced.

Modified:07.11.12

File Size:235 KB

Energy conversion efficiency at maximum output power, which embodies the essential characteristics of heat engines, is the main focus of the present work. The so-called Curzon and Ahlborn efficiency ηCA is commonly believed to be an absolute reference for real heat engines; however, a different but general expression for the case of stochastic heat engines, ηSS, was recently found and then extended to low-dissipation engines. The discrepancy between ηCA and ηSS is here analyzed considering different irreversibility sources of heat engines, of both internal and external types. To this end, we choose a thermoelectric generator operating in the strong-coupling regime as a physical system to qualitatively and quantitatively study the impact of the nature of irreversibility on the efficiency at maximum output power. In the limit of pure external dissipation, we obtain ηCA, while ηSS corresponds to the case of pure internal dissipation. A continuous transition between from one extreme to the other, which may be operated by tuning the different sources of irreversibility, also is evidenced.

Thermoelectric internal current loops inside inhomogeneous systems

Uploaded:07.11.12

Modified:07.11.12

File Size:140 KB

**Authors:** Y. Apertet, H. Ouerdane, C. Goupil and Ph. Lecoeur

Considering a system composed of two different thermoelectric modules electrically and thermally connected in parallel, we demonstrate that the inhomogeneities of the thermoelectric properties of the materials may cause the appearance of an electrical current, which develops inside the system.We show that this current increases the effective thermal conductance of the whole system.We also discuss the significance of a recent finding concerning a reported new electrothermal effect in inhomogeneous bipolar semiconductors, in light of our results.

Modified:07.11.12

File Size:140 KB

Considering a system composed of two different thermoelectric modules electrically and thermally connected in parallel, we demonstrate that the inhomogeneities of the thermoelectric properties of the materials may cause the appearance of an electrical current, which develops inside the system.We show that this current increases the effective thermal conductance of the whole system.We also discuss the significance of a recent finding concerning a reported new electrothermal effect in inhomogeneous bipolar semiconductors, in light of our results.

Optimal working conditions for thermoelectric generators with realistic thermal coupling

Uploaded:07.11.12

Modified:07.11.12

File Size:384 KB

**Authors: **Y. Apertet1, H. Ouerdane, O. Glavatskaya, C. Goupil and P. Lecoeur

We study how maximum output power can be obtained from a thermoelectric generator (TEG) with non-ideal heat exchangers. We demonstrate with an analytic approach based on a force-flux formalism that the sole improvement of the intrinsic characteristics of thermoelectric modules including the enhancement of the figure of merit is of limited interest: the constraints imposed by the working conditions of the TEG must be considered on the same footing. Introducing an effective thermal conductance we derive the conditions which permit maximization of both efficiency and power production of the TEG dissipatively coupled to heat reservoirs. Thermal impedance matching must be accounted for as well as electrical impedance matching in order to maximize the output power. Our calculations also show that the thermal impedance does not only depend on the thermal conductivity at zero electrical current: it also depends on the TEG figure of merit. Our analysis thus yields both electrical and thermal conditions permitting optimal use of a thermoelectric generator.

Modified:07.11.12

File Size:384 KB

We study how maximum output power can be obtained from a thermoelectric generator (TEG) with non-ideal heat exchangers. We demonstrate with an analytic approach based on a force-flux formalism that the sole improvement of the intrinsic characteristics of thermoelectric modules including the enhancement of the figure of merit is of limited interest: the constraints imposed by the working conditions of the TEG must be considered on the same footing. Introducing an effective thermal conductance we derive the conditions which permit maximization of both efficiency and power production of the TEG dissipatively coupled to heat reservoirs. Thermal impedance matching must be accounted for as well as electrical impedance matching in order to maximize the output power. Our calculations also show that the thermal impedance does not only depend on the thermal conductivity at zero electrical current: it also depends on the TEG figure of merit. Our analysis thus yields both electrical and thermal conditions permitting optimal use of a thermoelectric generator.

Interactions of neutral semipermeable shells in asymmetric electrolyte solutions

Uploaded:17.10.12

Modified:17.10.12

File Size:423 KB

**Authors:** Vladimir Lobaskin, Artem N. Bogdanov and Olga I. Vinogradova

We study the ionic equilibria and interactions of neutral semi-permeable spherical shells immersed in electrolyte solutions, including polyions. Although the shells are uncharged, only one type of ion of the electrolyte can permeate them, thus leading to a steric charge separation in the system. This gives rise to a charge accumulation inside the shell and a build up of concentration-dependent shell potential, which converts into a disjoining pressure between the neighboring shells. These are quantified using the Poisson–Boltzmann and integral equations theories. In particular, we show that in a case of low valency electrolytes, interactions between shells are repulsive and can be sufficiently strong to stabilize the shell dispersion. In contrast, the charge correlation effects in solutions of polyvalent ions result in attractions between the shells, with can lead to their aggregation.

Modified:17.10.12

File Size:423 KB

We study the ionic equilibria and interactions of neutral semi-permeable spherical shells immersed in electrolyte solutions, including polyions. Although the shells are uncharged, only one type of ion of the electrolyte can permeate them, thus leading to a steric charge separation in the system. This gives rise to a charge accumulation inside the shell and a build up of concentration-dependent shell potential, which converts into a disjoining pressure between the neighboring shells. These are quantified using the Poisson–Boltzmann and integral equations theories. In particular, we show that in a case of low valency electrolytes, interactions between shells are repulsive and can be sufficiently strong to stabilize the shell dispersion. In contrast, the charge correlation effects in solutions of polyvalent ions result in attractions between the shells, with can lead to their aggregation.

Tensorial slip of superhydrophobic channels

Uploaded:17.10.12

Modified:17.10.12

File Size:1 MB

**Authors**: Sebastian Schmieschek, Aleksey V. Belyaev, Jens Harting and Olga I. Vinogradova

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.

Modified:17.10.12

File Size:1 MB

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.

Effective slip boundary conditions for arbitrary onedimensional surfaces

Uploaded:17.10.12

Modified:17.10.12

File Size:659 KB

**Authors:** Evgeny S. Asmolov and Olga I. Vinogradova

In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip b(y), varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, 2b(y). A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

Modified:17.10.12

File Size:659 KB

In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip b(y), varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, 2b(y). A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

Anisotropic flow in striped superhydrophobic channels

Uploaded:17.10.12

Modified:17.10.12

File Size:504 KB

Modified:17.10.12

File Size:504 KB

**Authors:**

Jiajia Zhou, Aleksey V. Belyaev, Friederike Schmid and Olga I. Vinogradova

We report results of dissipative particle dynamics simulations and develop a semi-analytical theory of an anisotropic flow in a parallel-plate channel with two superhydrophobic striped walls. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. It allows us to optimize area fractions, slip lengths, channel thickness, and texture orientation to maximize a transverse flow. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations, and may also find applications in passive microfluidic mixing.

Electrostatic interaction of neutral semi-permeable membranes

Uploaded:17.10.12

Modified:17.10.12

File Size:566 KB

**Authors:**

*Olga I. Vinogradova, Lyderic Bocquet, Artem N. Bogdanov, Roumen Tsekov and Vladimir Lobaskin*

We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semipermeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the nonlinear Poisson–Boltzmann equation, we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van’t Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson–Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions. Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semi-permeable membranes.

Modified:17.10.12

File Size:566 KB

We consider an osmotic equilibrium between bulk solutions of polyelectrolyte bounded by semipermeable membranes and separated by a thin film of salt-free liquid. Although the membranes are neutral, the counter-ions of the polyelectrolyte molecules permeate into the gap and lead to a steric charge separation. This gives rise to a distance-dependent membrane potential, which translates into a repulsive electrostatic disjoining pressure. From the solution of the nonlinear Poisson–Boltzmann equation, we obtain the distribution of the potential and of ions. We then derive an explicit formula for the pressure exerted on the membranes and show that it deviates from the classical van’t Hoff expression for the osmotic pressure. This difference is interpreted in terms of a repulsive electrostatic disjoining pressure originating from the overlap of counterion clouds inside the gap. We also develop a simplified theory based on a linearized Poisson–Boltzmann approach. A comparison with simulation of a primitive model for the electrolyte is provided and does confirm the validity of the theoretical predictions. Beyond the fundamental result that the neutral surfaces can repel, this mechanism not only helps to control the adhesion and long-range interactions of living cells, bacteria, and vesicles, but also allows us to argue that electrostatic interactions should play enormous role in determining behavior and functions of systems bounded by semi-permeable membranes.

Effective slip boundary conditions for arbitrary

onedimensional surfaces

Uploaded:17.10.12

Modified:17.10.12

File Size:659 KB

**Authors:**

*Evgeny S. Asmolov and Olga I. Vinogradova*

Modified:17.10.12

File Size:659 KB

In many applications it is advantageous to construct effective slip boundary conditions, which could fully characterize flow over patterned surfaces. Here we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary scalar slip *b(y)*, varying in only one direction. We derive general expressions for eigenvalues of the effective slip-length tensor, and show that the transverse component is equal to half of the longitudinal one, with a two times larger local slip, *2b(y)*. A remarkable corollary of this relation is that the flow along any direction of the one-dimensional surface can be easily determined, once the longitudinal component of the effective slip tensor is found from the known spatially non-uniform scalar slip.

Tensorial slip of superhydrophobic channels

Uploaded:17.10.12

Modified:17.10.12

File Size:1 MB

**Authors:**

*Sebastian Schmieschek, Aleksey V. Belyaev, Jens Harting and Olga I. Vinogradova*

Modified:17.10.12

File Size:1 MB

We describe a generalization of the tensorial slip boundary condition, originally justified for a thick (compared to texture period) channel, to any channel thickness. The eigenvalues of the effective slip-length tensor, however, in general case become dependent on the gap and cannot be viewed as a local property of the surface, being a global characteristic of the channel. To illustrate the use of the tensor formalism we develop a semianalytical theory of an effective slip in a parallel-plate channel with one superhydrophobic striped and one hydrophilic surface. Our approach is valid for any local slip at the gas sectors and an arbitrary distance between the plates, ranging from a thick to a thin channel. We then present results of lattice Boltzmann simulations to validate the analysis. Our results may be useful for extracting effective slip tensors from global measurements, such as the permeability of a channel, in experiments or simulations.

Interactions of neutral semipermeable shells in asymmetric electrolyte solutions

Modified:17.10.12

File Size:423 KB

We study the ionic equilibria and interactions of neutral semi-permeable spherical shells immersed in electrolyte solutions, including polyions. Although the shells are uncharged, only one type of ion of the electrolyte can permeate them, thus leading to a steric charge separation in the system. This gives rise to a charge accumulation inside the shell and a build up of concentration-dependent shell potential, which converts into a disjoining pressure between the neighboring shells. These are quantified using the Poisson–Boltzmann and integral equations theories. In particular, we show that in a case of low valency electrolytes, interactions between shells are repulsive and can be sufficiently strong to stabilize the shell dispersion. In contrast, the charge correlation effects in solutions of polyvalent ions result in attractions between the shells, with can lead to their aggregation.

Optimum inhomogeneity of local lattice distortions

in La2CuO4+Y

Uploaded:03.09.12

Modified:03.09.12

File Size:1 MB

Modified:03.09.12

File Size:1 MB

Electronic functionalities in materials from silicon to transition metal oxides are, to a large extent, controlled by defects and their relative arrangement. Outstanding examples are the oxides of copper, where defect order is correlated with their high superconducting transition temperatures. The oxygen defect order can be highly inhomogeneous, even in optimal superconducting samples, which raises the question of the nature of the sample regions where the order does not exist but which nonetheless form the "glue" binding the ordered regions together. Here we use scanning X-ray microdiffraction (with a beam 300 nm in diameter) to show that for La2CuO4+y , the glue regions contain incommensurate modulated local lattice distortions, whose spatial extent is most pronounced for the best superconducting samples. For an underdoped single crystal with mobile oxygen interstitials in the spacer La2CuO4+y layers intercalated between the CuO2 layers, the incommensurate modulated local lattice distortions form droplets anticorrelated with the ordered oxygen interstitials, and whose spatial extent is most pronounced for the best superconducting samples. In this simplest of high temperature superconductors, there are therefore not one, but two networks of ordered defects which can be tuned to achieve optimal superconductivity. For a given stoichiometry, the highest transition temperature is obtained when both the ordered oxygen and lattice defects form fractal patterns, as opposed to appearing in isolated spots. We speculate that the relationship between material complexity and superconducting transition temperature Tc is actually underpinned by a fundamental relation between Tc and the distribution of ordered defect networks supported by the materials.

Spontaneous Symmetry Breaking in a Polariton and Photon Laser

Uploaded:04.07.12

Modified:04.07.12

File Size:2 MB

**Authors:**

*H. Ohadi, E. Kammann, T. C. H. Liew, K. G. Lagoudakis, A.V. Kavokin and P. G. Lagoudakis*

We report on the simultaneous observation of spontaneous symmetry breaking and long-range spatial coherence both in the strong- and the weak-coupling regime in a semiconductor microcavity. Under pulsed excitation, the formation of a stochastic order parameter is observed in polariton and photon lasing regimes. Single-shot measurements of the Stokes vector of the emission exhibit the buildup of stochastic polarization. Below threshold, the polarization noise does not exceed 10%, while above threshold we observe a total polarization of up to 50% after each excitation pulse, while the polarization averaged over the ensemble of pulses remains nearly zero. In both polariton and photon lasing regimes, the stochastic polarization buildup is accompanied by the buildup of spatial coherence. We find that the Landau criterion of spontaneous symmetry breaking and Penrose-Onsager criterion of long-range order for Bose-Einstein condensation are met in both polariton and photon lasing regimes.

Modified:04.07.12

File Size:2 MB

We report on the simultaneous observation of spontaneous symmetry breaking and long-range spatial coherence both in the strong- and the weak-coupling regime in a semiconductor microcavity. Under pulsed excitation, the formation of a stochastic order parameter is observed in polariton and photon lasing regimes. Single-shot measurements of the Stokes vector of the emission exhibit the buildup of stochastic polarization. Below threshold, the polarization noise does not exceed 10%, while above threshold we observe a total polarization of up to 50% after each excitation pulse, while the polarization averaged over the ensemble of pulses remains nearly zero. In both polariton and photon lasing regimes, the stochastic polarization buildup is accompanied by the buildup of spatial coherence. We find that the Landau criterion of spontaneous symmetry breaking and Penrose-Onsager criterion of long-range order for Bose-Einstein condensation are met in both polariton and photon lasing regimes.

Analytic model of effective screened Coulomb interactions in a multilayer system

Uploaded:13.10.11

Modified:13.10.11

File Size:459 KB

**Author:**

*H. Ouerdane*

The main objective of the present work is the development of an analytically tractable model of screened electron-electron and electron-exciton interactions in layered systems composed of two parallel semiconductor quantum wells separated by a dielectric layer. These systems are promising for superconductivity with excitons-polaritons, and spin manipulation. Polarization effects induced by the dielectric mismatch in the nanostructure are taken into account using the image charge method. The obtained analytic expressions are used to calculate screened electron-electron and electron-exciton interactions; these are compared to results computed using other recently published models.

Modified:13.10.11

File Size:459 KB

The main objective of the present work is the development of an analytically tractable model of screened electron-electron and electron-exciton interactions in layered systems composed of two parallel semiconductor quantum wells separated by a dielectric layer. These systems are promising for superconductivity with excitons-polaritons, and spin manipulation. Polarization effects induced by the dielectric mismatch in the nanostructure are taken into account using the image charge method. The obtained analytic expressions are used to calculate screened electron-electron and electron-exciton interactions; these are compared to results computed using other recently published models.

Error cancellation in the semiclassical calculation of the scattering length

Uploaded:13.10.11

Modified:13.10.11

File Size:278 KB

**Authors:**

*M.J. Jamieson, and H. Ouerdane*

We investigate the effects of two approximations concerning long range dispersion forces that are made in the derivation of the semiclassical formula for the scattering length of a pair of neutral atoms. We demonstrate numerically, using a published model interaction potential for a pair of Cs atoms in the 3Σ+ u molecular state, that the subsequent long range errors tend to cancel and we show, from an approximate analytical relationship, that the first order errors do indeed largely cancel.We suggest a hybrid method that combines quantum mechanical and semiclassical calculations. We explore its use in finding the scattering lengths of 7Li atoms and 133Cs atoms interacting via the Χ1Σ+ and a3Σ+ molecular potentials and we use it to demonstrate that the semiclassical formula fails for cold collisions of H atoms in the Χ1Σ+g molecular state because of the long range errors rather than because of inadequacies in describing the motion over the potential well semiclassically.

Modified:13.10.11

File Size:278 KB

We investigate the effects of two approximations concerning long range dispersion forces that are made in the derivation of the semiclassical formula for the scattering length of a pair of neutral atoms. We demonstrate numerically, using a published model interaction potential for a pair of Cs atoms in the 3Σ+ u molecular state, that the subsequent long range errors tend to cancel and we show, from an approximate analytical relationship, that the first order errors do indeed largely cancel.We suggest a hybrid method that combines quantum mechanical and semiclassical calculations. We explore its use in finding the scattering lengths of 7Li atoms and 133Cs atoms interacting via the Χ1Σ+ and a3Σ+ molecular potentials and we use it to demonstrate that the semiclassical formula fails for cold collisions of H atoms in the Χ1Σ+g molecular state because of the long range errors rather than because of inadequacies in describing the motion over the potential well semiclassically.

Coulomb singularities in scattering wave functions of spin-orbit-coupled states

Uploaded:13.10.11

Modified:13.10.11

File Size:375 KB

**Authors:**

*P. Bogdanski, and H. Ouerdane*

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl = 0,±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method.We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

Modified:13.10.11

File Size:375 KB

We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular momenta such that Δl = 0,±2. In these conditions, the two radial functions, components of a partial wave associated to two values of the angular momentum l, satisfy a system of two second-order ordinary differential equations. We examine the difficulties arising in the analysis of the behavior of the regular solutions near the origin because of this coupling. First, we demonstrate that for a singularity of the first kind in the potential, one of the solutions is not amenable to a power series expansion. The use of the Lippmann-Schwinger equations confirms this fact: a logarithmic divergence arises at the second iteration. To overcome this difficulty, we introduce two auxilliary functions which, together with the two radial functions, satisfy a system of four first-order differential equations. The reduction of the order of the differential system enables us to use a matrix-based approach, which generalizes the standard Frobenius method.We illustrate our analysis with numerical calculations of coupled scattering wave functions in a solid-state system.

Parameters for Cold Collisions of Lithium and Caesium Atoms

Uploaded:13.10.11

Modified:03.09.12

File Size:419 KB

**Authors:**

*Jamieson M. J., Ouerdane H.*

We calculate the s-wave scattering length and effective range and the p-wave scattering volume for 7Li atoms interacting with 133Cs atoms via the Χ1Σ+ molecular potential. The length and volume are found by fitting the log-derivative of the zero energy wave function evaluated at short range to a long range expression that accounts for the leading van der Waals dispersion potential and then incorporating the remaining long range dispersion contributions to first order. The effective range is evaluated from a quadrature formula. The calculated parameters are checked from the zero energy limits of the scattering phase shifts. We comment on ill-conditioning in the calculated s-wave scattering length.

Modified:03.09.12

File Size:419 KB

We calculate the s-wave scattering length and effective range and the p-wave scattering volume for 7Li atoms interacting with 133Cs atoms via the Χ1Σ+ molecular potential. The length and volume are found by fitting the log-derivative of the zero energy wave function evaluated at short range to a long range expression that accounts for the leading van der Waals dispersion potential and then incorporating the remaining long range dispersion contributions to first order. The effective range is evaluated from a quadrature formula. The calculated parameters are checked from the zero energy limits of the scattering phase shifts. We comment on ill-conditioning in the calculated s-wave scattering length.

The Puzzle of Magnetic Resonance Effect on the Magnetic Compass of Migratory Birds

Uploaded:13.11.10

Modified:13.11.10

File Size:109 KB

**Author:**

*K.V. Kavokin*

Experiments on the effect of radio-frequency (RF) magnetic fields on the magnetic compass orientation of migratory birds are analyzed using the theory of magnetic resonance. The results of these experiments were earlier interpreted within the radical-pair model of magnetoreception. However, the consistent analysis shows that the amplitudes of the RF fields used are far too small to noticeably influence electron spins in organic radicals. Other possible agents that could mediate the birds’ response to the RF fields are discussed, but apparently no known physical system can be responsible for this effect.

Modified:13.11.10

File Size:109 KB

Experiments on the effect of radio-frequency (RF) magnetic fields on the magnetic compass orientation of migratory birds are analyzed using the theory of magnetic resonance. The results of these experiments were earlier interpreted within the radical-pair model of magnetoreception. However, the consistent analysis shows that the amplitudes of the RF fields used are far too small to noticeably influence electron spins in organic radicals. Other possible agents that could mediate the birds’ response to the RF fields are discussed, but apparently no known physical system can be responsible for this effect.

Induced currents, frozen charges and the quantum Hall effect breakdown

Uploaded:13.11.10

Modified:13.11.10

File Size:111 KB

**Authors:**

*K.V. Kavokin, M.E. Portnoi, A.J. Matthews, A. Usher, J. Gething, D.A. Ritchie, M.Y. Simmons*

Puzzling results obtained from torque magnetometry in the quantum Hall effect regime are presented, and a theory is proposed for their explanation. Magnetic moment saturation, which is usually attributed to the quantum Hall effect breakdown, is shown to be related to the charge redistribution across the sample.

File Size:111 KB

Puzzling results obtained from torque magnetometry in the quantum Hall effect regime are presented, and a theory is proposed for their explanation. Magnetic moment saturation, which is usually attributed to the quantum Hall effect breakdown, is shown to be related to the charge redistribution across the sample.

Spin relaxation of localized electrons in n-type semiconductors

Uploaded:13.11.10

Modified:13.11.10

File Size:416 KB

**Author:**

*K.V. Kavokin*

The mechanisms that determine spin relaxation times of localized electrons in impurity bands of n-type semiconductors are considered theoretically and compared with available experimental data. The relaxation time of the non-equilibrium angular momentum is shown to be limited either by hyperfine interaction, or by spin–orbit interaction in the course of exchange-induced spin diffusion. The energy relaxation time in the spin system is governed by phonon-assisted hops within pairs of donors with an optimal distance of about 4 Bohr radii. The spin correlation time of the donor-bound electron is determined either by exchange interaction with other localized electrons, or by spin-flip scattering of free conduction-band electrons. A possibility of optical cooling of the spin system of localized electrons is discussed.

Modified:13.11.10

File Size:416 KB

The mechanisms that determine spin relaxation times of localized electrons in impurity bands of n-type semiconductors are considered theoretically and compared with available experimental data. The relaxation time of the non-equilibrium angular momentum is shown to be limited either by hyperfine interaction, or by spin–orbit interaction in the course of exchange-induced spin diffusion. The energy relaxation time in the spin system is governed by phonon-assisted hops within pairs of donors with an optimal distance of about 4 Bohr radii. The spin correlation time of the donor-bound electron is determined either by exchange interaction with other localized electrons, or by spin-flip scattering of free conduction-band electrons. A possibility of optical cooling of the spin system of localized electrons is discussed.

Size dependent carrier recombination in ZnO nanocrystals

Uploaded:12.10.10

Modified:12.10.10

File Size:808 KB

**Authors:**

*G. Pozina, L. L. Yang, Q. X. Zhao, L. Hultman,1 and P. G. Lagoudakis*

Experimental and theoretical studies of fluorescence decay were performed for colloidal ZnO nanocrystals. The fluorescence lifetime reduces from 22 ps to 6 ps with decreasing nanocrystal radius. We postulate that non-radiative surface states dominate the carrier dynamics in small ZnO nanocrystals and perform Monte Carlo simulations incorporating carrier diffusion and carrier recombination to model the experimental fluorescence decay dynamics. The percentage of excitons undergoing nonradiative decay due to surface trapping is as high as 84% for nanocrystals with 8 nm radius, which explains the ultrafast decay dynamics observed in small ZnO nanostructures even at low temperatures.

Modified:12.10.10

File Size:808 KB

Experimental and theoretical studies of fluorescence decay were performed for colloidal ZnO nanocrystals. The fluorescence lifetime reduces from 22 ps to 6 ps with decreasing nanocrystal radius. We postulate that non-radiative surface states dominate the carrier dynamics in small ZnO nanocrystals and perform Monte Carlo simulations incorporating carrier diffusion and carrier recombination to model the experimental fluorescence decay dynamics. The percentage of excitons undergoing nonradiative decay due to surface trapping is as high as 84% for nanocrystals with 8 nm radius, which explains the ultrafast decay dynamics observed in small ZnO nanostructures even at low temperatures.

Ultrafast pump–probe dynamics in ZnSe-based semiconductor quantum wells

Uploaded:13.09.10

Modified:12.10.10

File Size:208 KB

**Authors:**

*H. Ouerdane, G. Papageorgiou, I. Galbraith, A. K. Kar, and B. S. Wherrett*

Pump–probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment–theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree–Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.

Modified:12.10.10

File Size:208 KB

Pump–probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment–theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree–Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.

Barnes slave-boson approach to the two-site single-impurity Anderson model with non-local interaction

Uploaded:13.09.10

Modified:12.10.10

File Size:402 KB

**Authors:**

*R. Fr´esard, H. Ouerdane and T. Kopp*

The Barnes slave-boson approach to the U = ∞ single-impurity Anderson model extended by a non-local Coulomb interaction is revisited. We demonstrate first that the radial gauge representation facilitates the treatment of such a non-local interaction by performing the exact evaluation of the path integrals representing the partition function, the impurity hole density and the impurity hole density autocorrelation function for a two-site cluster. The free energy is also obtained on the same footing. Next, the exact results are compared to their approximations at saddle-point level, and it is shown that the saddle point evaluation recovers the exact answer in the limit of strong non-local Coulomb interaction, while the agreement between both schemes remains satisfactory in a large parameter range.

Modified:12.10.10

File Size:402 KB

The Barnes slave-boson approach to the U = ∞ single-impurity Anderson model extended by a non-local Coulomb interaction is revisited. We demonstrate first that the radial gauge representation facilitates the treatment of such a non-local interaction by performing the exact evaluation of the path integrals representing the partition function, the impurity hole density and the impurity hole density autocorrelation function for a two-site cluster. The free energy is also obtained on the same footing. Next, the exact results are compared to their approximations at saddle-point level, and it is shown that the saddle point evaluation recovers the exact answer in the limit of strong non-local Coulomb interaction, while the agreement between both schemes remains satisfactory in a large parameter range.

Scattering parameters for cold Li–Rb and Na–Rb collisions derived from variable phase theory

Uploaded:13.09.10

Modified:12.10.10

File Size:73 KB

**Authors:**

*H. Ouerdane and M. J. Jamieson*

We show how the scattering phase shift, the s-wave scattering length, and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson’s theorem yields the number of bound states supported by a potential. We report results from a study of the heteronuclear alkali-metal dimers NaRb and LiRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.

Modified:12.10.10

File Size:73 KB

We show how the scattering phase shift, the s-wave scattering length, and the p-wave scattering volume can be obtained from Riccati equations derived in variable phase theory. We find general expressions that provide upper and lower bounds for the scattering length and the scattering volume. We show how, in the framework of the variable phase method, Levinson’s theorem yields the number of bound states supported by a potential. We report results from a study of the heteronuclear alkali-metal dimers NaRb and LiRb. We explore the mass dependence of the scattering data by considering all isotopomers and we calculate the numbers of bound states supported by the molecular potentials for each isotopomer.

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Photon emission induced by elastic exciton-carrier

scattering in semiconductor quantum wells

Uploaded:13.09.10

Modified:12.10.10

File Size:498 KB

**Authors:**

*H. Ouerdane, R. Varache, M.E. Portnoi and I. Galbraith*

We present a study of the elastic exciton-electron (X–e−) and exciton-hole (X–h) scattering processes in semiconductor quantum wells, including fermion exchange effects. The balance between the exciton and the free carrier populations within the electron-hole plasma is discussed in terms of ionization degree in the nondegenerate regime. Assuming a two-dimensional Coulomb potential statically screened by the free carrier gas, we apply the variable phase method to obtain the excitonic wavefunctions, which we use to calculate the 1s exciton-free carrier matrix elements that describe the scattering of excitons into the light cone where they can radiatively recombine. The photon emission rates due to the carrierassisted exciton recombination in semiconductor quantum-wells (QWs) at room temperature and in a low density regime are obtained from Fermi’s golden rule, and studied for mid-gap and wide-gap materials. The quantitative comparison of the direct and exchange terms of the scattering matrix elements shows that fermion exchange is the dominant mechanism of the exciton-carrier scattering process. This is confirmed by our analysis of the rates of photon emission induced by electron-assisted and hole-assisted exciton recombinations.

Modified:12.10.10

File Size:498 KB

We present a study of the elastic exciton-electron (X–e−) and exciton-hole (X–h) scattering processes in semiconductor quantum wells, including fermion exchange effects. The balance between the exciton and the free carrier populations within the electron-hole plasma is discussed in terms of ionization degree in the nondegenerate regime. Assuming a two-dimensional Coulomb potential statically screened by the free carrier gas, we apply the variable phase method to obtain the excitonic wavefunctions, which we use to calculate the 1s exciton-free carrier matrix elements that describe the scattering of excitons into the light cone where they can radiatively recombine. The photon emission rates due to the carrierassisted exciton recombination in semiconductor quantum-wells (QWs) at room temperature and in a low density regime are obtained from Fermi’s golden rule, and studied for mid-gap and wide-gap materials. The quantitative comparison of the direct and exchange terms of the scattering matrix elements shows that fermion exchange is the dominant mechanism of the exciton-carrier scattering process. This is confirmed by our analysis of the rates of photon emission induced by electron-assisted and hole-assisted exciton recombinations.

Photon emission induced by elastic exciton-carrier scattering in semiconductor quantum wells

Modified:12.10.10

File Size:498 KB

We present a study of the elastic exciton-electron (X–e−) and exciton-hole (X–h) scattering processes in semiconductor quantum wells, including fermion exchange effects. The balance between the exciton and the free carrier populations within the electron-hole plasma is discussed in terms of ionization degree in the nondegenerate regime. Assuming a two-dimensional Coulomb potential statically screened by the free carrier gas, we apply the variable phase method to obtain the excitonic wavefunctions, which we use to calculate the 1s exciton-free carrier matrix elements that describe the scattering of excitons into the light cone where they can radiatively recombine. The photon emission rates due to the carrierassisted exciton recombination in semiconductor quantum-wells (QWs) at room temperature and in a low density regime are obtained from Fermi’s golden rule, and studied for mid-gap and wide-gap materials. The quantitative comparison of the direct and exchange terms of the scattering matrix elements shows that fermion exchange is the dominant mechanism of the exciton-carrier scattering process. This is confirmed by our analysis of the rates of photon emission induced by electron-assisted and hole-assisted exciton recombinations.

Polariton-polariton scattering in microcavities: A microscopic theory

Uploaded:13.09.10

Modified:12.10.10

File Size:208 KB

**Authors:**

*M. M. Glazov, H. Ouerdane, L. Pilozzi, G. Malpuech, A. V. Kavokin and A. D’Andrea*

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wave functions is used to calculate the effective scattering-matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well.We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.

Modified:12.10.10

File Size:208 KB

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wave functions is used to calculate the effective scattering-matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well.We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.

Polariton-polariton scattering in microcavities: A

microscopic theory

Modified:12.10.10

File Size:208 KB

We apply the fermion commutation technique for composite bosons to polariton-polariton scattering in semiconductor planar microcavities. Derivations are presented in a simple and physically transparent fashion. A procedure of orthogonolization of the initial and final two-exciton state wave functions is used to calculate the effective scattering-matrix elements and the scattering rates. We show how the bosonic stimulation of the scattering appears in this full fermionic approach whose equivalence to the bosonization method is thus demonstrated in the regime of low exciton density. We find an additional contribution to polariton-polariton scattering due to the exciton oscillator strength saturation, which we analyze as well.We present a theory of the polariton-polariton scattering with opposite spin orientations and show that this scattering process takes place mainly via dark excitonic states. Analytical estimations of the effective scattering amplitudes are given.

Slave bosons in radial gauge: A bridge between path integral and Hamiltonian language

Uploaded:13.09.10

Modified:12.10.10

File Size:306 KB

**Authors:**

*Raymond Frésard, Henni Ouerdane, Thilo Kopp*

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green’s function of the physical electron and the projected Green’s function of the pseudofermion coincide. Correlation and Green’s functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green’s function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.

Modified:12.10.10

File Size:306 KB

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green’s function of the physical electron and the projected Green’s function of the pseudofermion coincide. Correlation and Green’s functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green’s function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.

Exciton-Polariton Mediated Superconductivity

Uploaded:01.09.10

Modified:12.10.10

File Size:499 KB

**Authors:**

*F. P. Laussy, A. V. Kavokin and I. A. Shelykh*

We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of an exciton-polariton Bose- Einstein condensate. We consider a model microcavity where a quantum well with a two-dimensional electron gas is sandwiched between two undoped quantum wells, where a polariton condensate is formed. We show that the critical temperature for superconductivity dramatically increases with the condensate population, opening a new route towards high-temperature superconductivity.

Modified:12.10.10

File Size:499 KB

We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of an exciton-polariton Bose- Einstein condensate. We consider a model microcavity where a quantum well with a two-dimensional electron gas is sandwiched between two undoped quantum wells, where a polariton condensate is formed. We show that the critical temperature for superconductivity dramatically increases with the condensate population, opening a new route towards high-temperature superconductivity.

Optical Spin Hall Effect

Uploaded:31.08.10

Modified:12.10.10

File Size:207 KB

**Authors:**

*A. Kavokin, G. Malpuech and M. Glazov*

A remarkable analogy is established between the well-known spin Hall effect and the polarization dependence of Rayleigh scattering of light in microcavities. This dependence results from the strong spin effect in elastic scattering of exciton polaritons: if the initial polariton state has a zero spin and is characterized by some linear polarization, the scattered polaritons become strongly spin polarized. The polarization in the scattered state can be positive or negative dependent on the orientation of the linear polarization of the initial state and on the direction of scattering. Very surprisingly, spin polarizations of the polaritons scattered clockwise and anticlockwise have different signs. The optical spin Hall effect is possible due to strong longitudinal-transverse splitting and finite lifetime of exciton polaritons in microcavities.

Modified:12.10.10

File Size:207 KB

A remarkable analogy is established between the well-known spin Hall effect and the polarization dependence of Rayleigh scattering of light in microcavities. This dependence results from the strong spin effect in elastic scattering of exciton polaritons: if the initial polariton state has a zero spin and is characterized by some linear polarization, the scattered polaritons become strongly spin polarized. The polarization in the scattered state can be positive or negative dependent on the orientation of the linear polarization of the initial state and on the direction of scattering. Very surprisingly, spin polarizations of the polaritons scattered clockwise and anticlockwise have different signs. The optical spin Hall effect is possible due to strong longitudinal-transverse splitting and finite lifetime of exciton polaritons in microcavities.

Quantum Theory of Spin Dynamics of Exciton-Polaritons in Microcavities

Uploaded:31.08.10

Modified:12.10.10

File Size:134 KB

**Authors:**

*K.V. Kavokin, I. A. Shelykh, A.V. Kavokin, G. Malpuech and P. Bigenwald*

We present the quantum theory of momentum and spin relaxation of exciton-polaritons in microcavities. We show that giant longitudinal-transverse splitting of the polaritons mixes their spin states, which results in beats between right- and left-circularly polarized photoluminescence of microcavities, as was recently experimentally observed [M. D. Martin et al., Phys. Rev. Lett. 89, 077402 (2002)]. This effect is strongly sensitive to the bosonic stimulation of polariton scattering.

Modified:12.10.10

File Size:134 KB

We present the quantum theory of momentum and spin relaxation of exciton-polaritons in microcavities. We show that giant longitudinal-transverse splitting of the polaritons mixes their spin states, which results in beats between right- and left-circularly polarized photoluminescence of microcavities, as was recently experimentally observed [M. D. Martin et al., Phys. Rev. Lett. 89, 077402 (2002)]. This effect is strongly sensitive to the bosonic stimulation of polariton scattering.

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