Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation

TL;DR

This paper introduces a classical field approach to model the thermodynamics of an interacting trapped Bose-Einstein gas near the critical temperature, emphasizing the role of observation and detection time in defining condensate and thermal cloud.

Contribution

It presents a novel technique to describe the condensate and thermal cloud as a single classical field in equilibrium, accounting for finite detection time effects.

Findings

The entire system can be modeled as a single classical field with nonlinear dynamics.

Steady states emerge from the dynamics, reflecting equilibrium conditions.

Observation process influences the division between condensate and thermal cloud.

Abstract

We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.