Density and current response functions in strongly disordered electron systems: Diffusion, electrical conductivity and Einstein relation

Details Density and current response functions in strongly disordered electron systems: Diffusion, electrical conductivity and Einstein relation Density and current response functions in strongly disordered electron systems: Diffusion, electrical conductivity and Einstein relation

2002-03-20

arxiv.org/abs/cond-mat/0203414v3

Eur. J. Phys. B 35 (2003) 77

Physics

Condensed Matter

Disordered Systems and Neural Networks

16 pages, REVTeX4, 6 EPS figures

Scientific paper

10.1140/epjb/e2003-00258-4

We study consequences of gauge invariance and charge conservation of an electron gas in a strong random potential perturbed by a weak electromagnetic field. We use quantum equations of motion and Ward identities for one- and two-particle averaged Green functions to establish exact relations between density and current response functions. In particular we find precise conditions under which we can extract the current-current correlation function from the density-density correlation function and vice versa. We use these results in two different ways to extend validity of a formula associating the density response function with the electrical conductivity from semiclassical equilibrium to quantum nonequilibrium systems. Finally we introduce quantum diffusion via a response relating the current with the negative gradient of the charge density. With the aid of this response function we derive a quantum version of the Einstein relation and prove the existence of the diffusion pole in the zero-temperature electron-hole correlation function with the the long-range spatial fluctuations controlled by the static diffusion constant.

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