The Landau--Ginzberg theory for the two-dimensional Bose gas

TL;DR

This paper develops a Landau-Ginzburg theoretical framework for the two-dimensional Bose gas, linking quantum vortex phenomena to phase transitions and macroscopic order parameters.

Contribution

It introduces a novel Landau-Ginzburg model for 2D Bose gases based on sheaf theory and superfluid phenomenology, elucidating vortex-driven phase transitions.

Findings

Quantum vortices precipitate phase transitions in 2D Bose gases.

A macroscopic order parameter emerges from vortex dynamics.

The theory connects sheaf theory with superfluid phase behavior.

Abstract

Using results from sheaf theory combined with the phenomenological theory of the two-dimensional superfluid, the precipitation of quantum vortices is shown to be the genesis of a macroscopic order parameter for a phase transition in two dimensions.