Energy level statistics in weakly disordered systems: from quantum to diffusive regime

TL;DR

This paper derives an expression for the energy level correlation function in weakly disordered metallic systems, bridging quantum and diffusive regimes, by incorporating localization corrections using supersymmetric sigma models.

Contribution

It introduces a non-perturbative derivation of the energy level correlation function applicable across regimes, extending previous perturbative results.

Findings

Derived a general expression valid for all energy differences

Confirmed consistency with previous perturbative results

Bridged quantum and diffusive regimes in disordered systems

Abstract

We calculate two-point energy level correlation function in weakly disorderd metallic grain with taking account of localization corrections to the universal random matrix result. Using supersymmetric nonlinear sigma model and exactly integrating out spatially homogeneous modes, we derive the expression valid for arbitrary energy differences from quantum to diffusive regime for the system with broken time reversal symmetry. Our result coincides with the one obtained by Andreev and Altshuler [Phys. Rev. Lett. 72, 902 (1995)] where homogeneous modes are perturbatively treated.