Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons

In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symm...

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Veröffentlicht in:	Archive for rational mechanics and analysis 2019-01, Vol.231 (1), p.63-89
Hauptverfasser:	Nguyen, Toan T., Tran, Minh-Binh
Format:	Artikel
Sprache:	eng
Schlagworte:	Boltzmann transport equation Bosons Classical Mechanics Complex Systems Fluid- and Aerodynamics Gaussian distribution Lower bounds Mathematical analysis Mathematical and Computational Physics Normal distribution Particle energy Physics Physics and Astronomy Theoretical
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Zusammenfassung:	In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.
ISSN:	0003-9527 1432-0673
DOI:	10.1007/s00205-018-1271-z