Non-perturbative approach to backscattering off a dynamical impurity in 1D Fermi systems

TL;DR

This paper develops a non-perturbative method to analyze how a time-dependent impurity affects electron backscattering in one-dimensional Fermi systems, revealing the impact on energy distribution.

Contribution

It introduces a combined Schwinger-Keldysh and adiabatic approach to study out-of-equilibrium backscattering effects non-perturbatively.

Findings

Backscattering distorts the energy density profile.

Impurity geometry influences energy distribution.

Method effectively captures non-perturbative effects.

Abstract

We investigate the problem of backscattering off a time-dependent impurity in a one-dimensional electron gas. By combining the Schwinger-Keldysh method with an adiabatic approximation in order to deal with the corresponding out of equilibrium Dirac equation, we compute the total energy density (TED) of the system. We show how the free fermion TED is distorted by the backscattering amplitude and the geometry of the impurity.