Electron-electron interaction in a disordered electron gas in non-equilibrium

Alexei L. Efros, F. G. Pikus

P. T. Landsberg, J. S. Shiner

R. Katilius, S. V. Gantsevich, V. D. Kagan +1 more

Here we develop a mathematical apparatus to describe quasi-classical fluctuations in a non-equilibrium electron gas with electron-electron collisions. We substantiate the method by deriving, from general principles of quantum kinetics, an equation recently proposed by us for an equal-time electron-electron correlation function. The derivation is performed using the kinetic diagram technique. In degenerate non-equilibrium gas, the theory predicts that there exists a specific equal-time correlation between electrons. Due to the prevalence of small-angle electron-electron scattering, the equation in question takes a rather simple and treatable form (the Coulomb-type electron-electron interaction stands out against the background of all other types of interaction as one that does not generate, in the framework of quasi-classical approach, any direct exchange effects).

Karen Michaeli

Thibault Scoquart

This thesis manuscript is devoted to different aspects of the non-equilibrium dynamics of a moving two-dimensional ultra-cold Bose gas, under the simultaneous action of a spatially disordered potential and interactions between particles. In the absence of interactions, the momentum distribution of the gas is the sum of two well-known components: a classical, diffusive background made of particles multiply scattered by the disorder, and a coherent backscattering interference peak (CBS peak), consequence of the weak localization phenomenon. In the presence of weak interactions, mean field simulations show that these two contributions evolve in time. This evolution is described by two coupled kinetic equations, which we derive using a microscopic quantum transport theory. These predict the destruction of the CBS peak by an effective dephasing mechanism, and the thermalization of the diffusive background. As the interaction strength increases, the effects of disorder become negligible, and the dynamics of the gas resembles that of a superfluid. In this regime, the gas quickly enters a so-called "pre-thermal" state: the spatial correlations g_1 decrease algebraically and propagate along a light cone, in accordance with theoretical predictions. Finally, at long times, our simulations describe the global evolution of the system towards a thermal equilibrium state, characterized by a Kosterlitz-Thouless transition separating a normal fluid state from a superfluid state. Some properties of this phase transition, resulting from the non-equilibrium evolution in the presence of disorder, are discussed.

Jialin Zhu, R. Riklund, K. A. Chao