Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo like fidelity plays a central role and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-body localization and coupled kicked rotors, and saturates to a value that depends on the relative coin and walker space dimensions. In a coin dominated scenario, the chaos can thermalize the quantum walk to typical random states such that the entanglement saturates at the Haar averaged Page value, unlike in a walker dominated case when atypical states seem to be produced.
Dynamical zero modes and boundary dependence in dynamical quantum phase transitions
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理北京国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Center for Theoretical Physics of Complex Systems, Institute for Basic Science（复杂系统理论物理中心，基础科学研究院）；Department of Physics and Astronomy, Center for Materials Theory, Rutgers University（物理与天文学系，材料理论中心，罗格斯大学）；Physics Department, Columbia University（物理系，哥伦比亚大学）；Basic Science Program, Korea University of Science and Technology (UST)（基础科学项目，韩国科学技术院）
Macroscopic thermalization by unitary time evolution in the weakly perturbed two-dimensional Ising model --- An application of the Roos-Sugimoto-Teufel-Tumulka-Vogel theory
Department of Physics, Gakushuin University（学习院大学物理系）
Reduced fidelities for free fermions out of equilibrium: From dynamical quantum phase transitions to Mpemba effect
Laboratoire d’Annecy de Physique Théorique (LAPTh), CNRS, Université Savoie Mont Blanc（萨瓦-蒙布朗大学）；Dipartimento di Fisica, Università di Pisa, and INFN Sezione di Pisa（比萨大学）
