Finite phase coherence time of a bosonic quantum field at the Boltzmann equilibrium

TL;DR

This paper develops a quantum field model for a weakly interacting Bose gas, revealing a unique time scale for quantum coherence decay and transitions between equilibrium states, based on particle coherence times.

Contribution

It introduces a non-local order parameter approach to quantify coherence times and transition dynamics in a dilute Bose-Einstein condensate at equilibrium.

Findings

Coherence decay times are characterized by a single time variable.

A numerical estimate for the unit time scale of particle propagation is provided.

The model links coherence times to transitions between maximum entropy equilibrium states.

Abstract

A quantitative quantum field approach with non-local order parameters is presented for a very weakly interacting, dilute Bose gas. Within the presented model, which assumes the constraint of particle number conservation at constant average energy in the canonical ensemble, it is shown that both coherent oscillations, as well as decay times of quantum coherence for the forward and backward propagating components of the quantum field created by the atomic cloud of a very weakly interacting Bose-Einstein condensate, are defined by a unique time variable. Within the present numerical theory, a quantitative estimate for the unit time scale for time propagation of a particle in a very weakly interacting Bose gas is derived from the coherence time of the wave field and it is illustrated that this time scale defines a unit time for transitions between different realizations of the Boltzmann equilibrium as defined by the maximum entropy from the vanishing of the chemical potential.