Local enhancement of the mean-field approximation for bosons
报告人：张景宣 (清华大学)
时间：2024-12-30 16:00-17:00
地点：智华楼313
Abstract: The nonlinear Hartree equation describes the macroscopic dynamics of initially factorized $N$ boson states as $N\to\infty$. Global estimates on the rate of convergence of the microscopic quantum mechanical evolution towards the limiting Hartree dynamics have been derived in the seminal works of Erdos-Schlein-Yau, Rodianski-Schlein, etc. Here we derive a local enhancement of the mean-field approximation: At positive distance $\rho>0$ from the initial BEC, the mean-field approximation error at time $t\leq \rho/v$ is bounded as $\rho^{-n}$, for arbitrarily large $n\geq 1$. This is a consequence of new ballistic propagation bounds on the quantum fluctuations around the Hartree states. Based on joint work with M. Lemm and S. Rademacher.
