Return probability: Exponential versus Gaussian decay

TL;DR

This paper investigates the decay behavior of return probability in interacting particle systems, comparing Gaussian and exponential regimes through analytical and numerical methods, with implications for quantum computation models.

Contribution

It provides a detailed analytical and numerical comparison of Gaussian and exponential decay regimes of return probability in interacting systems.

Findings

Gaussian decay occurs under certain conditions.

Exponential decay dominates in other regimes.

Numerical data confirms analytical predictions.

Abstract

We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the Gaussian decay of the return probability, and another one is the well known regime of the exponential decay. Our analytical estimates are confirmed by the numerical data obtained for two models with random interaction. In view of these results, we also briefly discuss the dynamical model which was recently proposed for the implementation of a quantum computation.