A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases
A reaction network approach to the convergence to equilibrium of quantum Boltzmann equations for Bose gases
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DOI：
10.1051/cocv/2021079
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发表时间：
2016-08
期刊：
影响因子：
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通讯作者：
G. Craciun;Minh-Binh Tran
中科院分区：
文献类型：
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作者：
G. Craciun;Minh-Binh Tran
当被捕获的玻色气体的温度低于玻色-爱因斯坦转变温度且高于绝对零时，该气体由两种不同的成分组成：玻色-爱因斯坦凝聚物和热激发云。激发的动力学可以通过量子玻尔兹曼模型来描述。我们在量子玻尔兹曼模型和化学反应网络之间建立了联系。我们证明这些量子玻尔兹曼模型的离散微分方程收敛到平衡点。此外，这一点对于满足相同守恒定律的所有初始条件来说都是唯一的。在证明中，我们采用了一种环面动力系统方法，类似于证明全局吸引子猜想的方法，来研究量子动力学方程的平衡收敛。
When the temperature of a trapped Bose gas is below the Bose-Einstein transition temperature and above absolute zero, the gas is composed of two distinct components: the Bose-Einstein condensate and the cloud of thermal excitations. The dynamics of the excitations can be described by quantum Boltzmann models. We establish a connection between quantum Boltzmann models and chemical reaction networks. We prove that the discrete differential equations for these quantum Boltzmann models converge to an equilibrium point. Moreover, this point is unique for all initial conditions that satisfy the same conservation laws. In the proof, we then employ a toric dynamical system approach, similar to the one used to prove the global attractor conjecture, to study the convergence to equilibrium of quantum kinetic equations.