BEC for a Coupled Two-type Hard Core Bosons Model

TL;DR

This paper analyzes a solvable model of two types of hard core bosons, demonstrating Bose-Einstein condensation, spontaneous gauge symmetry breaking, and characterizing quantum normal modes and plasmon frequencies.

Contribution

It provides a complete analysis of the equilibrium states and proves the existence of Bose-Einstein condensation in a coupled two-type hard core bosons model.

Findings

Existence of Bose-Einstein condensation in the model

Identification of two-fold degeneracy of plasmon frequencies

Spontaneous gauge symmetry breakdown as the underlying cause

Abstract

We study a solvable model of two types hard core Bose particles. A complete analysis is given of its equilibrium states including the proof of existence of Bose-Einstein condensation. The plasmon frequencies and the quantum normal modes corresponding to these frequencies are rigorously constructed. In particular we show a two-fold degeneracy of these frequencies. We show that all this results from spontaneous gauge symmetry breakdown.