中科院数学与系统科学研究院

数学研究所

学术报告

非线性泛函分析研讨班

报告人：张景宣(清华大学)

题  目：Localization estimates for quantum dynamics I: a generic framework

时  间：2024.9.26（星期四）13：30-14：30

地  点：N817

摘  要： We present our recent works on localization estimates for quantum dynamics described by time-dependent linear Schrödinger equations. Whereas the latter are known to lack strict light cones, we prove the existence of effective light cones, obtain explicit upper bounds on the maximal speed of particle transport and information propagation, and derive long-time decay estimates for the probability leakage away from the effective light cones. This is the first part of two talks and the focus is on a generic framework of localization theory for abstract Schrödinger equations. In the second part we will focus on applications to dynamical upper bounds in various concrete models arising from many-body quantum systems. Based on joint works with I.M. Sigal, M. Lemm, J. Faupin, and others.