Fidelity decay in interacting two-level boson systems: Freezing and revivals

TL;DR

This paper investigates how fidelity decay in two-level boson systems exhibits freezing and revivals, linking the periodicity of revivals to the interaction range, supported by analytical and numerical evidence.

Contribution

It provides an analytical and numerical study of fidelity freeze and revivals in bosonic systems, revealing the connection between revival periodicity and interaction range.

Findings

Fidelity exhibits a freeze with periodic revivals at integer multiples of the Heisenberg time.

The revival period is an integer fraction of the Heisenberg time, depending on the interaction range.

Numerical results confirm the analytical predictions about fidelity behavior.

Abstract

We study the fidelity decay in the $k$-body embedded ensembles of random matrices for bosons distributed in two single-particle states, considering the reference or unperturbed Hamiltonian as the one-body terms and the diagonal part of the $k$-body embedded ensemble of random matrices, and the perturbation as the residual off-diagonal part of the interaction. We calculate the ensemble-averaged fidelity with respect to an initial random state within linear response theory to second order on the perturbation strength, and demonstrate that it displays the freeze of the fidelity. During the freeze, the average fidelity exhibits periodic revivals at integer values of the Heisenberg time $t_H$. By selecting specific $k$-body terms of the residual interaction, we find that the periodicity of the revivals during the freeze of fidelity is an integer fraction of $t_H$, thus relating the period of the revivals with the range of the interaction $k$ of the perturbing terms. Numerical calculations confirm the analytical results.