Influence Functional for Decoherence of Interacting Electrons in Disordered Conductors

TL;DR

This paper rederives and clarifies the influence functional approach for electron decoherence in disordered conductors, demonstrating its equivalence to diagrammatic perturbation theory and improving the treatment of recoil effects.

Contribution

It provides a more accurate and simplified derivation of the influence functional approach, aligning it with standard perturbation results and enhancing the understanding of decoherence mechanisms.

Findings

Reproduces the standard decoherence rate result

Shows equivalence to diagrammatic Keldysh perturbation theory

Improves recoil effect treatment in the influence functional approach

Abstract

We have rederived the controversial influence functional approach of Golubev and Zaikin (GZ) for interacting electrons in disordered metals in a way that allows us to show its equivalence, before disorder averaging, to diagrammatic Keldysh perturbation theory. By representing a certain Pauli factor (1-2 rho) occuring in GZ's effective action in the frequency domain (instead of the time domain, as GZ do), we also achieve a more accurate treatment of recoil effects. With this change, GZ's approach reproduces, in a remarkably simple way, the standard, generally accepted result for the decoherence rate. -- The main text and appendix A.1 to A.3 of the present paper have already been published previously; for convenience, they are included here again, together with five additional, lengthy appendices containing relevant technical details.