Quantum Monte Carlo simulations of a particle in a random potential

TL;DR

This study uses Quantum Monte Carlo simulations to analyze a quantum particle in a one-dimensional disordered potential, exploring its glassy behavior and quantum fluctuations at finite temperature.

Contribution

It provides the first simulation-based analysis of quantum particles in disordered potentials, comparing results with analytical predictions and examining quantum effects on glassiness.

Findings

Sample to sample fluctuations of mean square displacement quantified

Quantum fluctuations influence the system's glassy behavior

Simulation results align with analytical predictions

Abstract

In this paper we carry out Quantum Monte Carlo simulations of a quantum particle in a one-dimensional random potential (plus a fixed harmonic potential) at a finite temperature. This is the simplest model of an interface in a disordered medium and may also pertain to an electron in a dirty metal. We compare with previous analytical results, and also derive an expression for the sample to sample fluctuations of the mean square displacement from the origin which is a measure of the glassiness of the system. This quantity as well as the mean square displacement of the particle are measured in the simulation. The similarity to the quantum spin glass in a transverse field is noted. The effect of quantum fluctuations on the glassy behavior is discussed.