Parametric correlations versus fidelity decay: the symmetry breaking case

TL;DR

This paper derives relations between fidelity decay and parametric energy correlations in random matrix ensembles where time-reversal symmetry is broken, extending previous symmetry-conserving results.

Contribution

It provides a theoretical framework linking fidelity decay and energy correlations in symmetry-breaking scenarios, which was not previously established.

Findings

Established a simple relation between fidelity decay and energy correlations with broken time-reversal symmetry.

Extended symmetry-conserving results to symmetry-breaking cases in random matrix theory.

Provides analytical expressions applicable to quantum systems with broken time-reversal invariance.

Abstract

We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.