论文标题
平均玻色子在正温度下的动力学
Dynamics of mean-field bosons at positive temperature
论文作者
论文摘要
我们研究了陷阱电位关闭后，最初捕获的弱相互作用的bose气体的时间演变。最近在Arxiv：2009.00992中表明，相互作用的捕获气体的Gibbs状态的单粒子密度矩阵被以$ n $为中期的订单为$ n $，为$ n \ to \ infty $，是理想的气体之一，由凝聚力波功能替代了Hartree Energy功能的最小化剂。我们表明，这种结构在以下意义上相对于多体演化是稳定的：可以根据凝结波函数的时间依赖性Hartree方程以及热激发粒子的自由演化来近似动力学。我们作品的主要技术新颖性是使用Hartree-fock-Bogoliubov方程来定义波动动态。
We study the time evolution of an initially trapped weakly interacting Bose gas at positive temperature, after the trapping potential has been switched off. It has been recently shown in arXiv:2009.00992 that the one-particle density matrix of Gibbs states of the interacting trapped gas is given, to leading order in $N$, as $N \to \infty$, by the one of the ideal gas, with the condensate wave function replaced by the minimizer of the Hartree energy functional. We show that this structure is stable with respect to the many-body evolution in the following sense: the dynamics can be approximated in terms of the time-dependent Hartree equation for the condensate wave function and in terms of the free evolution for the thermally excited particles. The main technical novelty of our work is the use of the Hartree-Fock-Bogoliubov equations to define a fluctuation dynamics.
