Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons
Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons
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DOI：
10.1007/s00205-018-1271-z
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发表时间：
2016-05
影响因子：
2.5
通讯作者：
Toan T. Nguyen;Minh-Binh Tran
中科院分区：
文献类型：
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作者：
Toan T. Nguyen;Minh-Binh Tran
在本文中，我们考虑量子玻尔兹曼方程，它描述了受激原子与凝聚态之间的相互作用。碰撞积分是接管的能量流形，具有粒子能量的 Bogoliubov 色散定律的完整形式。我们证明量子玻尔兹曼方程的非负径向对称解自下而上受高斯分布限制，且时间均匀。
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.