Difference in BoseEinstein Condensation
of Conserved and Unconserved Particles¹

V. I. Yukalov

Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscov region, 141980 Russia

Received October 7, 2011; in final form, November 25, 2011; published online June 12, 2012

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. Illus-
trations 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 mag-
nons, 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 non-
equilibrium 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 equi-
librium may favor the condensation of unconserved quasiparticles, but suppresses the condensate fraction of
conserved particles.

DOI: 10.1134/S1054660X12070171

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