Fluctuations and stochastic processes in one-dimensional many-body quantum systems

TL;DR

This paper investigates fluctuation behaviors in one-dimensional many-body quantum systems of interacting bosons, comparing quantum noise and thermal effects, and develops a semiclassical Ornstein-Uhlenbeck process model to analyze phase correlations and interference statistics.

Contribution

It introduces a semiclassical Ornstein-Uhlenbeck process framework for thermal fluctuations and compares it with Luttinger-liquid theory in one-dimensional bosonic systems.

Findings

Thermal and quantum fluctuation regimes are characterized.

The semiclassical model accurately describes phase correlations.

Interference distributions match theoretical predictions.

Abstract

We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled and compare with the Luttinger-liquid theory.