论文标题
时间均匀的时间收敛到Bose-Einstein凝结，以使弱相互作用的玻色气体具有外部电势
Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential
论文作者
论文摘要
我们考虑在平均野外状态下具有外部电势的三个维度上弱相互作用的玻色子的气体。假设我们系统的初始状态是产品状态，我们表明在一体密度矩阵的痕量拓扑中，可以通过对相应的Hartree类型方程的解决方案来描述系统的动力学。使用Hartree类型方程的分散估计，我们获得了一个误差项，该误差项在时间上均匀。此外，误差项对粒子数的依赖性是最佳的。我们还考虑了平均场式和毛比特人的总体状态之间的一类中间度机制，其中误差项在时间上是统一的，但在粒子数量中却不是最佳的。
We consider a gas of weakly interacting bosons in three dimensions subject to an external potential in the mean field regime. Assuming that the initial state of our system is a product state, we show that in the trace topology of one-body density matrices, the dynamics of the system can be described by the solution to the corresponding Hartree type equation. Using a dispersive estimate for the Hartree type equation, we obtain an error term that is uniform in time. Moreover, the dependence of the error term on the particle number is optimal. We also consider a class of intermediate regimes between the mean field regime and the Gross-Pitaevskii regime, where the error term is uniform in time but not optimal in the number of particles.
