Exact Fidelity and Full Fidelity Statistics in Regular and Chaotic Surroundings

TL;DR

This paper derives exact formulas for fidelity and participation ratio in quantum systems, analyzing their long-term behavior and revealing phenomena like fidelity revival and non-ergodicity.

Contribution

It provides analytical expressions for fidelity and participation ratio, and explores their distributions and phenomena in regular and chaotic environments.

Findings

Fidelity revival observed in long-term dynamics

Enhanced non-ergodicity in certain regimes

Analytical and numerical agreement on distribution functions

Abstract

For a prepared state exact expressions for the time dependent mean fidelity as well as for the mean inverse paricipation ratio are obtained analytically. The distribution function of fidelity in the long time limit and of inverse participation ratio are studied numerically and analytically. Surprising features like fidelity revival and enhanced non--ergodicity are observed. The role of the coupling coefficients and of complexity of background is studied as well.