Effective dynamics of disordered quantum systems

TL;DR

This paper derives general equations for the average quantum dynamics in disordered systems, accounting for how disorder impacts coherence through effective parameters linked to the Hamiltonian's spectral properties.

Contribution

It introduces a unified framework for modeling ensemble-averaged quantum evolution in disordered systems, incorporating spectral and eigenvector disorder effects.

Findings

Effective evolution equations for disordered quantum systems.

Disorder influences coherence via tailored effective couplings and rates.

Application to spectral and isotropic eigenvector disorder cases.

Abstract

We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates which encode the specific statistical properties of the Hamiltonian's eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.