Nonexponential fidelity decay in isolated interacting quantum systems

TL;DR

This paper investigates nonexponential fidelity decay in isolated quantum systems, identifying Gaussian, Bessel, and cosine squared decay behaviors under different conditions, revealing complex dynamics beyond typical exponential decay.

Contribution

It characterizes three distinct nonexponential decay scenarios in finite quantum systems, linking them to specific physical conditions and types of perturbations.

Findings

Gaussian decay in strongly perturbed two-body systems

Bessel decay associated with sparse random matrices

Cosine squared decay from local perturbations and energy-time uncertainty

Abstract

We study isolated finite interacting quantum systems after an instantaneous perturbation and show three scenarios in which the probability for finding the initial state later in time (fidelity) decays nonexponentially, often all the way to saturation. The decays analyzed involve Gaussian, Bessel of the first kind, and cosine squared functions. The Gaussian behavior emerges in systems with two-body interactions in the limit of strong perturbation. The Bessel function, associated with the evolution under full random matrices, is obtained with surprisingly sparse random matrices. The cosine squared behavior, established by the energy-time uncertainty relation, is approached after a local perturbation in space.