Relaxation of an electron system: Conserving approximation

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 semiclassical 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 generalized hydrodynamic equations applicable to arbitrary frequencies.