The Boltzmann Equation for Bose–Einstein Particles: Velocity Concentration and Convergence to Equilibrium

2005 ◽  
Vol 119 (5-6) ◽  
pp. 1027-1067 ◽  
Author(s):  
Xuguang Lu
Keyword(s):  
Boltzmann Equation ◽  
Convergence To Equilibrium ◽  
The Boltzmann Equation ◽  
Bose Einstein

scholarly journals On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

2009 ◽  
Vol 135 (4) ◽  
pp. 681-736 ◽  
Author(s):  
Eric A. Carlen ◽  
Maria C. Carvalho ◽  
Xuguang Lu
Keyword(s):  
Boltzmann Equation ◽  
Strong Convergence ◽  
Convergence To Equilibrium ◽  
The Boltzmann Equation

On the Boltzmann Equation for 2D Bose-Einstein Particles

2011 ◽  
Vol 143 (5) ◽  
pp. 990-1019 ◽  
Author(s):  
Xuguang Lu ◽  
Xiangdong Zhang
Keyword(s):  
Boltzmann Equation ◽  
The Boltzmann Equation ◽  
Bose Einstein

Global existence and long time behavior of solutions of a quantum Boltzmann equation

2015 ◽  
Vol 13 (06) ◽  
pp. 611-643
Author(s):  
Mingying Zhong
Keyword(s):  
Boltzmann Equation ◽  
Global Existence ◽  
Einstein Condensation ◽  
Convergence To Equilibrium ◽  
Time Behavior ◽  
Quantum Boltzmann Equation ◽  
Long Time ◽  
Energy Variable ◽  
Bose Einstein

In this paper, we study a quantum Boltzmann equation with a harmonic oscillator for isotropic gases of bosons and fermions, respectively. This model comes from physics literatures (see, e.g., [M. Holland, J. Williams and J. Cooper, Bose–Einstein condensation: Kinetic evolution obtained from simulated trajectories, Phys. Rev. A 55 (1997) 3670–3677]). The distribution function, i.e. the solution, is discrete in the energy variable. We give the classification of equilibria of the equation for bosons and fermions, respectively, and prove the global existence, uniqueness and the strong convergence to equilibrium for solutions of the equation.

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