Difference in Bose-Einstein condensation of conserved and unconserved particles

TL;DR

This paper analyzes the fundamental differences between Bose-Einstein condensation of conserved and unconserved particles, emphasizing their conditions, examples, and the effects of equilibrium and nonequilibrium states.

Contribution

It provides a comprehensive classification and comparison of Bose-Einstein condensation for conserved versus unconserved particles, including various quasiparticles and their condensation conditions.

Findings

Conserved particles can form both equilibrium and nonequilibrium condensates.

Unconserved particles condense only in nonequilibrium systems with external pumping.

Elementary excitations like bogolons and phonons do not condense.

Abstract

The peculiarities in the Bose-Einstein condensation of particles and quasiparticles are discussed. The difference between the condensation of conserved and unconserved particles is analyzed. A classification of quasiparticles is given. The emphasis is made on the ability of particles and quasiparticles to condense. Illustrations include: general Bose-condensed atomic systems, such as ensembles of trapped atoms, Bose gases with conserved and unconserved number of atoms, vibrating atoms in double-well lattices, Holstein-Primakoff magnons, Schwinger bosons, slave bosons, and the condensation of singletons and triplons. The basic difference is that the system of particles, whose total number is conserved, can form equilibrium as well as nonequilibrium condensates, while unconserved particles can condense only in a nonequilibrium system subject to external pumping supporting the density of these particles sufficient for their condensation. The examples of such a nonequilibrium condensation of unconserved particles are the Bose-Einstein condensation of excitons, polaritons, and photons. Elementary collective excitations, such as bogolons and phonons, being self-consistently defined, do not condense. Magnons cannot condense in equilibrium systems. Controversies, existing in literature with regard to the Bose-Einstein condensation of some quasiparticles, are explained. Pushing a system out of equilibrium may favor the condensation of unconserved quasiparticles, but suppresses the condensate fraction of conserved particles.