论文标题
平均场状态中Fröhlich动力学的标准近似
Norm approximation for the Fröhlich dynamics in the mean-field regime
论文作者
论文摘要
我们研究了弗里希里奇汉密尔顿的时间演变，在平均场极限中，许多颗粒弱夫妇逐渐降低到量化的声子场。假设颗粒最初是在玻色的凝结物中，并且声子场的激发最初处于连贯的状态，我们提供了一个有效的动力学，只要粒子数量很大，它近似于规范的时间演化的多体状态。近似是由乘积状态给出的，该产品状态根据Landau-Pekar方程进化，并通过Bogoliubov动力学校正。此外，我们从[拱门扩展了结果。配给。机械。肛门。 240，383-417（2021）]关于时间的近似值，在痕量 - 构型拓扑中演变为多体状态到较大的多体初始状态，并提高了收敛速度。
We study the time evolution of the Fröhlich Hamiltonian in a mean-field limit in which many particles weakly couple to the quantized phonon field. Assuming that the particles are initially in a Bose-Einstein condensate and that the excitations of the phonon field are initially in a coherent state we provide an effective dynamics which approximates the time evolved many-body state in norm, provided that the number of particles is large. The approximation is given by a product state which evolves according to the Landau-Pekar equations and which is corrected by a Bogoliubov dynamics. In addition, we extend the results from [Arch. Ration. Mech. Anal. 240, 383-417 (2021)] about the approximation of the time evolved many-body state in trace-norm topology to a larger class of many-body initial states with an improved rate of convergence.
