The dephasing rate formula in the many body context

TL;DR

This paper presents a simple method for calculating the dephasing rate in many-fermion systems that accurately incorporates Pauli blocking, extending to strong interactions and relevant for disordered metals.

Contribution

It introduces a straightforward approach based on Fermi's golden rule that enforces the Pauli principle in many-fermion dephasing calculations, including strong-coupling effects.

Findings

Enforces Pauli blocking in dephasing rate calculations.

Connects the approach to diagrammatic methods.

Addresses strong-coupling scenarios in disordered metals.

Abstract

We suggest a straightforward approach to the calculation of the dephasing rate in a fermionic system, which correctly keeps track of the crucial physics of Pauli blocking. Starting from Fermi's golden rule, the dephasing rate can be written as an integral over the frequency transferred between system and environment, weighted by their respective spectral densities. We show that treating the full many-fermion system instead of a single particle automatically enforces the Pauli principle. Furthermore, we explain the relation to diagrammatics. Finally, we show how to treat the more involved strong-coupling case when interactions appreciably modify the spectra. This is relevant for the situation in disordered metals, where screening is important.