Random Hamiltonian in thermal equilibrium

TL;DR

This paper introduces a new framework for studying disordered quantum systems in thermal equilibrium using a dynamical model that equilibrates Hamiltonians into a canonical distribution, enabling calculation of quantum observable averages.

Contribution

It proposes a novel dynamical approach combining gradient flow and Brownian fluctuation to model Hamiltonian equilibration in disordered quantum systems.

Findings

Framework successfully models Hamiltonian equilibration.

Enables calculation of quenched and annealed averages.

Provides insights into thermal properties of disordered quantum systems.

Abstract

A framework for the investigation of disordered quantum systems in thermal equilibrium is proposed. The approach is based on a dynamical model--which consists of a combination of a double-bracket gradient flow and a uniform Brownian fluctuation--that `equilibrates' the Hamiltonian into a canonical distribution. The resulting equilibrium state is used to calculate quenched and annealed averages of quantum observables.