Solving a nonlinear analytical model for bosonic equilibration

TL;DR

This paper presents an exact solution to a nonlinear integrable model describing bosonic system equilibration, accounting for thermal tail buildup, phase transition, and particle-number conservation during cooling.

Contribution

It introduces a novel exact solution to a previously devised nonlinear model, incorporating boundary conditions relevant for Bose-Einstein distributions and particle conservation.

Findings

Exact solution for bosonic equilibration model

Accounts for thermal tail and phase transition

Includes particle-number conservation during cooling

Abstract

An integrable nonlinear model for the time-dependent equilibration of a bosonic system that has been devised earlier is solved exactly with boundary conditions that are appropriate for a truncated Bose-Einstein distribution, and include the singularity at $\epsilon = \mu$. The buildup of a thermal tail during evaporative cooling, as well as the transition to the condensed state are accounted for. To enforce particle-number conservation during the cooling process with an energy-dependent density of states for a three-dimensional thermal cloud, a time-dependent chemical potential is introduced.