Fidelity decay and entropy production in many-particle systems after random interaction quench

TL;DR

This paper investigates how spin influences fidelity decay and entropy production in many-particle quantum systems after a random interaction quench, using embedded Gaussian orthogonal ensemble models.

Contribution

It introduces an analytical framework based on EGOE to describe short-time dynamics and the saturation time of entropy, highlighting spin dependence in relaxation processes.

Findings

Fidelity decay and entropy production are significantly affected by spin.

Analytical formulas for entropy saturation time agree with numerical results.

Spin influences the relaxation dynamics in both fermionic and bosonic systems.

Abstract

We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic(bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin $S$. The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving $S$ for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time ($t_{sat}$) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.