Truncation method for Green's functions in time-dependent fields

TL;DR

This paper introduces a truncation method for calculating Green's functions in time-dependent electric fields, enabling analysis of scattering and conductivity in complex quantum systems.

Contribution

It develops a novel approach to compute Green's functions under time-dependent fields using matrix truncation and Floquet theory, applicable to disordered and scattering systems.

Findings

Exact solutions for Green's functions in specific models

Relation between inelastic scattering rate and AC conductivity

Method's applicability near metal-insulator transitions

Abstract

We investigate the influence of a time dependent, homogeneous electric field on scattering properties of non-interacting electrons in an arbitrary static potential. We develop a method to calculate the (Keldysh) Green's function in two complementary approaches. Starting from a plane wave basis, a formally exact solution is given in terms of the inverse of a matrix containing infinitely many 'photoblocks' which can be evaluated approximately by truncation. In the exact eigenstate basis of the scattering potential, we obtain a version of the Floquet state theory in the Green's functions language. The formalism is checked for cases such as a simple model of a double barrier in a strong electric field. Furthermore, an exact relation between the inelastic scattering rate due to the microwave and the AC conductivity of the system is derived which in particular holds near or at a metal-insulator transition in disordered systems.