Spectral Correlation and Response functions in Quantum Dots

TL;DR

This paper establishes a universal relation linking density of states fluctuations and response functions in quantum dots, applicable across various symmetry classes and disordered regimes, extending beyond traditional Wigner-Dyson statistics.

Contribution

It derives a general, robust relation between correlators of density of states fluctuations and response functions applicable to diverse quantum systems.

Findings

Valid for quantum chaotic systems with different symmetries

Extends to disordered metals with finite conductance

Applicable to Anderson insulators with large localization length

Abstract

We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the crossover region between the universality classes. This relation is much more robust than Wigner-Dyson statistics; its validity extends to disordered metals with finite conductance and even to the Anderson insulators with large localization length.