Parametric Statistics of Individual Energy Levels in Random Hamiltonians

TL;DR

This paper develops a general framework for analyzing how individual energy levels in disordered and chaotic quantum systems with unitary symmetry respond to external perturbations, focusing on parametric statistics.

Contribution

It introduces a novel method to compute universal intra-level velocity correlations and level shift distributions under arbitrary external influences.

Findings

Derived universal intra-level velocity correlation functions

Calculated distribution of level shifts for external perturbations

Applicable to disordered and chaotic quantum systems with unitary symmetry

Abstract

We establish a general framework to explore parametric statistics of individual energy levels in disordered and chaotic quantum systems of unitary symmetry. The method is applied to the calculation of the universal intra-level parametric velocity correlation function and the distribution of level shifts under the influence of an arbitrary external perturbation.