Local Enhancement of the Mean-field Approximation for Bosons
Time: 2024-12-24
Published By: He Liu
Speaker(s): Jingxuan Zhang(Tsinghua University)
Time: 16:00-17:00 December 30, 2024
Venue: Room 313, Zhihua Building
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.
