A simple model of Bose-Einstein condensation of interacting particles

TL;DR

This paper introduces a simple interacting particle model for Bose-Einstein condensation, highlighting that interactions fundamentally alter thermodynamic behavior and cannot be approximated by ideal gas models.

Contribution

It presents a novel simple model demonstrating that interactions prevent the ideal Bose gas limit and resolve thermodynamic inconsistencies in Bose-Einstein condensation.

Findings

Interactions prevent power series expansion in coupling constant.

Ideal Bose gas limit is not attainable through zero interaction.

Interactions resolve thermodynamic and fluctuation issues in the condensate.

Abstract

A simple model of Bose-Einstein condensation of interacting particles is proposed. It is shown that in the condensate state the dependence of thermodynamic quantities on the interaction constant does not allow an expansion in powers of the coupling constant. Therefore it is impossible to pass to the Einstein model of condensation in an ideal Bose gas by means of a limiting passage, setting the interaction constant to zero. The account for the interaction between particles eliminates difficulties in the description of condensation available in the model of an ideal gas, which are connected with fulfillment of thermodynamic relations and an infinite value of the particle number fluctuation in the condensate phase.