Decoherence in weak localization II: Bethe-Salpeter calculation of Cooperon

TL;DR

This paper confirms and extends the calculation of decoherence effects in weak localization by deriving and approximately solving a Bethe-Salpeter equation for the Cooperon, ensuring divergence-free results for the decoherence rate.

Contribution

It introduces a diagrammatic Bethe-Salpeter approach to compute the Cooperon, including self-energy and vertex corrections, providing a divergence-free method for decoherence analysis.

Findings

Bethe-Salpeter equation accurately describes Cooperon decoherence.

Decoherence rate obtained from first-order Cooperon in position-time space.

Method is divergence-free and independent of prior influence functional approach.

Abstract

This is the second in a series of two papers (I and II) on the problem of decoherence in weak localization. In paper I, we discussed how the Pauli principle could be incorporated into an influence functional approach for calculating the Cooperon propagator and the magnetoconductivity. In the present paper II, we check and confirm the results so obtained by diagrammatically setting up a Bethe-Salpeter equation for the Cooperon, which includes self-energy and vertex terms on an equal footing and is free from both infrared and ultraviolet divergencies. We then approximately solve this Bethe-Salpeter equation by the Ansatz C(t) = C^0 (t) e^{-F(t)}, where the decay function F(t) determines the decoherence rate. We show that in order to obtain a divergence-free expression for the decay function F(t), it is sufficient to calculate C^1 (t), the Cooperon in the position-time representation to first order in the interaction. Paper II is independent of paper I and can be read without detailed knowledge of the latter.