Microscopic theory of a phase transition in a critical region: Bose-Einstein condensation in an interacting gas

TL;DR

This paper develops a microscopic theory describing the continuous formation of Bose-Einstein condensates in an interacting gas across the entire critical region, unifying disordered and ordered phases.

Contribution

It introduces exact fundamental equations for the condensate wave function and Green functions valid throughout the critical region, extending traditional low-temperature equations.

Findings

Derived exact equations valid inside and outside the critical region

Unified description of phase transition across the critical region

Applicable to other phase transitions in condensed matter and quantum fields

Abstract

We present a microscopic theory of the second order phase transition in an interacting Bose gas that allows one to describe formation of an ordered condensate phase from a disordered phase across an entire critical region continuously. We derive the exact fundamental equations for a condensate wave function and the Green functions, which are valid both inside and outside the critical region. They are reduced to the usual Gross-Pitaevskii and Beliaev-Popov equations in a low-temperature limit outside the critical region. The theory is readily extendable to other phase transitions, in particular, in the physics of condensed matter and quantum fields.