Semiclassical approach to fidelity amplitude

TL;DR

This paper employs semiclassical theory to analyze the average fidelity amplitude in quantum chaotic systems, elucidating its behavior under different perturbation regimes and validating findings with numerical simulations.

Contribution

It introduces a semiclassical framework to study fidelity decay in quantum chaos, connecting extreme dynamical and perturbation limits.

Findings

Analytical explanation of fidelity decay in extreme regimes

Identification of Lyapunov decay under strong chaos

Numerical results bridging theoretical limits

Abstract

The fidelity amplitude is a quantity of paramount importance in echo type experiments. We use semiclassical theory to study the average fidelity amplitude for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit --attained approximately by strongly chaotic systems-- and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us bridge the gap between both extreme cases.