We introduce a dissipation term in the Gross-Pitaevskii equation that describes the stimulated relaxation of condensed bosons due to scattering with a different type of particles. This situation applies to Bose-Einstein condensates of quasi-particles in the solid state, such as magnons and excitons. Our model is compatible with the phenomenology of superfluidity: supercurrents are stable up to a critical speed and decay when they are faster.

arXiv:1007.5453Jul 30, 20101 citation

arXiv:1310.0180 · Physical Review A

Hybrid Boltzmann–Gross-Pitaevskii theory of Bose-Einstein condensation and superfluidity in open driven-dissipative systems

Dmitry D. Solnyshkov, Hugo Terças, K. Dini, G. Malpuech

Published Mar 20, 2014• 90 citations

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Abstract

DOI: 10.1103/physreva.89.033626

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Kinetic Theory of Bose-Einstein Condensation and Superfluidity in Open Driven-Dissipative Systems

Dmitry D. Solnyshkov, Hugo Terças, K. Dini +1 more

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Energy relaxation in the Gross-Pitaevskii equation

Michiel Wouters, Vincenzo Savona

arXiv:1007.5453Jul 30, 20101 citation

\omega = q v_\ell

ω = q v ℓ . In a ring geometry, the quantization of angular momentum leads to a discrete set of velocities, which suppresses the availability of resonant states and strongly inhibits Landau damping. In contrast, in the continuous limit

R \rightarrow \infty

R → ∞ , the spectrum becomes quasi-continuous and the standard Landau damping mechanism is recovered, establishing a direct connection between kinetic resonances and the energetic criterion for superfluidity. We further analyze the role of Bogoliubov depletion by considering a finite-width angular momentum distribution. Although resonant states formally exist in this case, we show that, for flow velocities below the sound velocity, the phase-space distribution does not provide the gradients required for energy transfer, and the superfluid current remains dynamically stable. Our results provide a unified phase-space interpretation of superfluidity, highlighting the role of angular momentum quantization and the structure of the distribution function in determining the stability of persistent currents. Graphic abstract Phase-space interpretation of superfluid stability in a ring Bose-Einstein condensate. For flow velocities below the sound velocity, resonant phase-space trajectories are unavailable and the superflow remains stable, whereas above the sound velocity resonant coupling becomes possible, leading to kinetic instability