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Relaxation of an Electron System : Conserving Approximation

G. S. Atwal·N. W. Ashcroft
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Abstract

The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is that the local electron equilibrium distribution must have a space- and time-dependent chemical potential, drift velocity and temperature. Both quantum kinetic and semi-classical arguments are given, and we calculate and analyze the corresponding analytical d-dimensional dielectric function. Dynamical correlation, arising from relaxation effects, is shown to soften the plasmon dispersion of both two- and three-dimensional systems. Finally, we consider the consequences for a hydrodynamic theory of a d-dimensional interacting electron gas, and by incorporating the competition between relaxation and inertial effects we derive generalised hydrodynamic equations applicable to arbitrary frequencies.

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G. S. Atwal, N. W. Ashcroft. 2002-09-18. Relaxation of an Electron System : Conserving Approximation. https://doi.org/10.1103/physrevb.65.115109

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