No-Go Theorem for Quasiparticle BEC

TL;DR

This paper proves a no-go theorem for quasiparticle Bose-Einstein condensation (BEC) using operator algebra methods, showing BEC cannot occur under certain conditions in the van Hove model.

Contribution

It establishes a rigorous no-go theorem for quasiparticle BEC by analyzing operator algebras and infrared divergences, extending previous self-consistency approaches.

Findings

Time cluster properties prevent BEC in the van Hove model.

Infrared divergences with nonlinear dispersion exclude BEC on the reduced algebra.

The treatment of divergences relates to the ideal theory of the resolvent algebra.

Abstract

We discuss a no-go theorem for Bose-Einstein condensation (BEC) of quasiparticles (phonons) from the viewpoint of operator algebras, using the van Hove model. The $\beta$-KMS states of the van Hove model satisfy the self-consistency condition of arXiv:1207.4621. However, the self-consistency condition is a constraint concerning the definition of the field, and is insufficient to establish the no-go theorem for BEC. In this paper, we prove the no-go theorem for BEC via two routes. First, imposing time cluster properties on the $\beta$-KMS states precludes BEC. Second, under nonlinear dispersion with $s > 2$, the treatment of infrared divergences automatically reduces the algebra of physical observables, and BEC is mathematically excluded on the reduced algebra. In particular, the latter property admits an interpretation in terms of the ideal theory of the resolvent algebra.