Statistics and dynamics of the center of mass coordinate in a quantum liquid

TL;DR

This paper investigates the behavior of the center of mass in a one-dimensional interacting Fermi gas, revealing universal dynamics in the metallic phase and differences across phases, with implications for experiments in ultracold gases.

Contribution

It combines numerics and bosonization to show the universal autocorrelation behavior of the center of mass in the metallic phase of a quantum liquid.

Findings

Variance of center of mass vanishes in insulating phases

Autocorrelation function exhibits persistent oscillations in the metallic phase

Full counting statistics follow a normal distribution even in small systems

Abstract

Motivated by recent experiments in ultracold gases, we focus on the properties of the center of mass coordinate of an interacting one dimensional Fermi gas, displaying several distinct phases. While the variance of the center of mass vanishes in insulating phases such as phase separated and charge density wave phases, it remains finite in the metallic phase, which realizes a Luttinger liquid. By combining numerics with bosonization, we demonstrate that the autocorrelation function of the center of mass coordinate is universal throughout the metallic phase. It exhibits persistent oscillations and its short time dynamics reveal important features of the quantum liquid, such as the Luttinger liquid parameter and the renormalized velocity. The full counting statistics of the center of mass follows a normal distribution already for small systems. Our results apply to non-integrable systems as well and are within experimental reach for e.g. carbon nanotubes and cold atomic gases.