Response of a Fermi gas to time-dependent perturbations: Riemann-Hilbert approach at non-zero temperatures

TL;DR

This paper extends the Riemann-Hilbert approach to finite temperatures for calculating response functions in nonadiabatically perturbed Fermi gases, enabling exact analysis of nonequilibrium phenomena.

Contribution

It introduces a finite temperature Riemann-Hilbert framework and demonstrates its equivalence to the zero temperature case for response function calculations.

Findings

Finite temperature Riemann-Hilbert problem defined and solved.

Equivalence established between finite and zero temperature problems.

Applied to analyze nonequilibrium Fermi-edge singularity at finite temperatures.

Abstract

We provide an exact finite temperature extension to the recently developed Riemann-Hilbert approach for the calculation of response functions in nonadiabatically perturbed (multi-channel) Fermi gases. We give a precise definition of the finite temperature Riemann-Hilbert problem and show that it is equivalent to a zero temperature problem. Using this equivalence, we discuss the solution of the nonequilibrium Fermi-edge singularity problem at finite temperatures.