PhD Defense Jingxuan Zhang
PhD Candidate: Jingxuan Zhang
Title: Localization theory for propagation of quantum information
Abstract:
In this thesis, we propose a generic framework of localization theory for the propagation of information in non-relativistic quantum mechanics. Specifically, for a large class of quantum dynamics that are known to lack strict light cones, we prove the existence of effective light cones, obtain explicit upper bounds on the maximal propagation speed of quantum
information, and derive long-time decay estimates for the probability leakage away from the effective light cones. Our method, geometric in nature, is based on monotonicity estimates and adiabatic approximations using certain observables that identify the spacetime localization property of evolving states. Applications of our framework include energy-dependent
effective light cones for continuous Markovian open quantum systems and Lieb-Robinsontype bounds for long-range interacting bosonic many-body quantum systems.
Advisor: Niels Martin Møller, University of Copenhagen
Assessment committee:
Jan Philip Solovej, University of Copenhagen, Chair
Phan Thanh Nam, Ludwig Maximilian University of Munich
Robert Seiringer, Institute of Science and Technology Austria