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.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.

arXiv:1207.4621Laser PhysicsJun 12, 201229 citations

Bose-Einstein condensation in nonequilibrium systems

H. Haug, H. Kranz

The European Physical Journal BJun 1, 198329 citations

Thermalization of a weakly interacting Bose gas in a disordered trap

Che-Hsiu Hsueh, Makoto Tsubota, Wen Chin Wu

Previously we numerically showed that thermalization can occur in an oscillating Bose-Einstein condensate (BEC) with a disordered harmonic trap when healing length $ξ$ of the condensate is shorter than the correlation length $σ_{D}$ of the disorder [see, for example, the experiment reported in Phys. Rev. A \textbf{82}, 033603 (2010)]. In this work, we investigate the weakly interacting or Anderson localization regime $ξ>σ_{D}$ and show that the oscillating BEC can also exhibit a relaxation process from nonequilibrium to equilibrium. In such an isolated quantum system, energy and particle number are conserved and the irreversible evolution towards thermodynamic equilibrium is induced by the disorder. The thermodynamic equilibrium is evidenced by the maximized entropy $S\left[n_{k}\right]$ in which the waveaction spectrum $n_{k}$ follows the Rayleigh-Jeans distribution. Besides, unlike a monotonic irreversible process of thermalization to equilibrium, the Fermi-Pasta-Ulam-Tsingou recurrence arises in this system, manifested by the oscillation of the non-equilibrium entropy.Previously we numerically showed that thermalization can occur in an oscillating Bose-Einstein condensate (BEC) with a disordered harmonic trap when healing length $ξ$ of the condensate is shorter than the correlation length $σ_{D}$ of the disorder [see, for example, the experiment reported in Phys. Rev. A \textbf{82}, 033603 (2010)]. In this work, we investigate the weakly interacting or Anderson localization regime $ξ>σ_{D}$ and show that the oscillating BEC can also exhibit a relaxation process from nonequilibrium to equilibrium. In such an isolated quantum system, energy and particle number are conserved and the irreversible evolution towards thermodynamic equilibrium is induced by the disorder. The thermodynamic equilibrium is evidenced by the maximized entropy $S\left[n_{k}\right]$ in which the waveaction spectrum $n_{k}$ follows the Rayleigh-Jeans distribution. Besides, unlike a monotonic irreversible process of thermalization to equilibrium, the Fermi-Pasta-Ulam-Tsingou recurrence arises in this system, manifested by the oscillation of the non-equilibrium entropy.

arXiv:1807.11047Jul 29, 20181 citation

Nonequilibrium Bose–Einstein condensates

Esteban A. Calzetta, B. L. Hu

Cambridge University Press eBooksNov 4, 20220 citations

Thermodynamics of Bose—Einstein Condensation

Premabrata Manna, Satadal Bhattacharyya

ResonanceSep 24, 20222 citations

Models for equilibrium BEC superradiance

Joseph V Pulé, André F. Verbeure, Valentin Anatol'evich Zagrebnov

We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose-Einstein condensation and superradiance. In this paper we formalise the model suggested by Ketterle et al in which the Bose condensate particles have a two level structure. We present a soluble microscopic Dicke type model describing a thermodynamically stable system. We find the equilibrium states of the system and compute the thermodynamic functions giving explicit formulae expressing the cooperative effect between Bose-Einstein condensation and superradiance.We study the effect of electromagnetic radiation on the condensate of a Bose gas. In an earlier paper we considered the problem for two simple models showing the cooperative effect between Bose-Einstein condensation and superradiance. In this paper we formalise the model suggested by Ketterle et al in which the Bose condensate particles have a two level structure. We present a soluble microscopic Dicke type model describing a thermodynamically stable system. We find the equilibrium states of the system and compute the thermodynamic functions giving explicit formulae expressing the cooperative effect between Bose-Einstein condensation and superradiance.

arXiv:math-ph/0410037Journal of Physics A Mathematical and GeneralJul 1, 20046 citations

Previously we numerically showed that thermalization can occur in an oscillating Bose-Einstein condensate (BEC) with a disordered harmonic trap when healing length

ξ

of the condensate is shorter than the correlation length

σ_{D}

of the disorder [see, for example, the experiment reported in Phys. Rev. A \textbf{82}, 033603 (2010)]. In this work, we investigate the weakly interacting or Anderson localization regime

ξ>σ_{D}

and show that the oscillating BEC can also exhibit a relaxation process from nonequilibrium to equilibrium. In such an isolated quantum system, energy and particle number are conserved and the irreversible evolution towards thermodynamic equilibrium is induced by the disorder. The thermodynamic equilibrium is evidenced by the maximized entropy

S\left[n_{k}\right]

in which the waveaction spectrum

n_{k}

follows the Rayleigh-Jeans distribution. Besides, unlike a monotonic irreversible process of thermalization to equilibrium, the Fermi-Pasta-Ulam-Tsingou recurrence arises in this system, manifested by the oscillation of the non-equilibrium entropy.