Non-Markovian response of complex quantum systems

TL;DR

This paper investigates the non-Markovian dynamics of complex quantum systems under external perturbations, revealing regimes of normal diffusion and ballistic behavior depending on memory time scales and correlations.

Contribution

It introduces a non-Markovian Fokker-Planck equation for quantum state occupancy using a random matrix approach, highlighting how diffusion regimes depend on correlation properties.

Findings

Normal diffusion occurs at small memory times with energy diffusion suppressed by matrix element correlations.

Large memory times lead to ballistic quantum dynamics.

Diffusion behavior is significantly affected by the energy distribution and correlations of the coupling matrix elements.

Abstract

We study the perturbative response of a complex quantum system on time changes of an external parameter $X$. The driven dynamics is treated in adiabatic basis of the system's Hamiltonian $\hat{H}[X]$. Within a random matrix approach we obtained non--Markovian Fokker--Planck equation for the occupancy of given adiabatic state. We observed normal diffusion regime of the driven quantum dynamics at quite small values of the memory time defined by the time scales of the $X$--correlations and energy--distribution of the coupling matrix elements $(\partial \hat{H}/\partial X)_{nm}$. Here the normal energy diffusion was found to drop out with the width of the matrix elements' energy--distribution and the diffusion may be significantly suppressed with the decrease of the correlations between the matrix elements. In the opposite limit of relatively large memory times we obtained ballistic regime of the dynamics.