Journal
KINETIC AND RELATED MODELS
Volume 8, Issue 3, Pages 493-531Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/krm.2015.8.493
Keywords
Quantum Boltzmann equation; rate of convergence to equilibrium; algebraic decay
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Funding
- MICINN, Spain [2011-29306-C02-00, MTM2011-29306-C02-00]
- Basque Government Grant [IT641-13, PI2010-04]
- ERC Advanced Grant [FP7-246775 NUMERIWAVES]
- MINECO, Spain [SEV-2013-0323]
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We consider an approximation of the linearised equation of the homogeneous Boltzmann equation that describes the distribution of quasipartides 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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