Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature

Miguel  Escobedo; Minh-Binh  Tran

doi:10.3934/krm.2015.8.493

Article Contents

2015, Volume 8, Issue 3: 493-531. Doi: 10.3934/krm.2015.8.493

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Convergence to equilibrium of a linearized quantum Boltzmann equation for bosons at very low temperature

Miguel Escobedo^1, and
Minh-Binh Tran^2,

1.
Departamento de Matemáticas, Universidad del País Vasco, (UPV/EHU), Apartado 644, E-48080 Bilbao
2.
Basque Center for Applied Mathematics, Mazarredo 14, E48009 Bilbao

Received: December 31, 2014

Revised: January 31, 2015

Published: August 2015

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Abstract

We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasiparticles in a dilute gas of bosons at low temperature. The corresponding collision frequency is neither bounded from below nor from above. We prove the existence and uniqueness of solutions satisfying the conservation of energy. We show that these solutions converge to the corresponding stationary state, at an algebraic rate as time tends to infinity.

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Mathematics Subject Classification: Primary: 35Q20, 45A05; Secondary: 47G10, 82B40, 82B40.

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