Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors

TL;DR

This paper introduces a new method called fictitious level dynamics to analyze spectral statistics in disordered conductors, linking energy level movements to impurity potential changes and deriving spectral correlations through novel theoretical approaches.

Contribution

The paper presents a new approach using fictitious dynamics and decoupling techniques to calculate spectral form factors and correlations in disordered conductors, including weak localization corrections.

Findings

Spectral correlations expressed via quantum return probability.

Weak localization corrections vanish to three-loop order in 2D systems.

Two methods yield consistent spectral statistics results.

Abstract

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.