2013/10/31 by D. D. Solnyshkov, Hugo Terças, H. Terças +3 · 2 citations
Physics and Astronomy · #Boltzmann constant #Boltzmann equation #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Dissipative system #Gross–Pitaevskii equation #Heat transfer #Physics #Quantum #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum mechanics #Semiclassical physics #Strong Light-Matter Interactions #Superfluidity #Thermal reservoir #cond-mat.mes-hall #cond-mat.quant-gas
paper · pdf · doi:10.1103/physreva.89.033626
arxiv created 2014/01/21 · openalex publication_date 2014/03/20 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We derive a theoretical model which describes Bose-Einstein condensation in an open driven-dissipative system. It includes external pumping of a thermal reservoir, finite lifetime of the condensed particles, and energy relaxation. The coupling between the reservoir and the condensate is described with semiclassical Boltzmann rates. This results in a dissipative term in the Gross-Pitaevskii equation for the condensate, which is proportional to the energy of the elementary excitations of the system. We analyze the main properties of a condensate described by this hybrid Boltzmann--Gross-Pitaevskii model, namely, dispersion of the elementary excitations, bogolon distribution function, first-order coherence, dynamic and energetic stability, and drag force created by a disorder potential. We find that the dispersion of the elementary excitations of a condensed state fulfills the Landau criterion of superfluidity. The condensate is dynamically and energetically stable as longs as it moves at a velocity smaller than the speed of excitations. First-order spatial coherence of the condensate is found to decay exponentially in one dimension and with a power law in two dimensions, similarly with the case of conservative systems. The coherence lengths are found to be longer due to the finite lifetime of the condensate excitations. We compare these properties with those of a condensate described by the popular ``diffusive'' models in which the dissipative term is proportional to the local condensate density. In the latter, the dispersion of excitations is diffusive which as soon as the condensate is put into motion implies finite mechanical friction and can lead to an energetic instability.