Surprising relations between parametric level correlations and fidelity decay

TL;DR

This paper uncovers unexpected links between fidelity decay and parametric level correlations in quantum systems, revealing power law decay near Heisenberg time and illustrating revivals through numerical simulations.

Contribution

It establishes novel relations between fidelity decay and cross form-factor using supersymmetry and random matrix theory, and demonstrates revivals via numerical analysis.

Findings

Power law decay near Heisenberg time influences fidelity revivals

Exact results connect parametric level correlations with fidelity decay

Numerical simulations confirm theoretical predictions in spin chains

Abstract

Unexpected relations between fidelity decay and cross form--factor, i.e., parametric level correlations in the time domain are found both by a heuristic argument and by comparing exact results, using supersymmetry techniques, in the framework of random matrix theory. A power law decay near Heisenberg time, as a function of the relevant parameter, is shown to be at the root of revivals recently discovered for fidelity decay. For cross form--factors the revivals are illustrated by a numerical study of a multiply kicked Ising spin chain.