Mathematics of thermalization in isolated quantum systems
 Date
 November 10 (Tue) at 16:00  18:10, 2020 (JST)
 Speaker

 Naoto Shiraishi (Assistant Professor, Faculty of Science Department of Physics, Gakushuin University)
 Venue
 via Zoom
 Language
 English
If an isolated macroscopic quantum system is left at a nonequilibrium state, then this system will relax to the unique equilibrium state, which is called thermalization. Most of quantum manybody systems thermalize, while some manybody systems including integrable systems do not thermalize. What determines the presence/absence of thermalization and how to understand thermalization from microscopic quantum mechanics are profound longstanding problems.
In the first part of my talk, I briefly review some established results of quantum thermalization. I first clarify the problem of thermalization in a mathematical manner, and then introduce several important results and insights: typicality of equilibrium states [1], relaxation caused by large effective dimension [2], and eigenstate thermalization hypothesis (ETH) [3,4] and weakETH [5].
In the second part of my talk, I explain some of my results. First, I introduce a model which is nonintegrable and thermalizes but does not satisfy the ETH [6,7]. This finding disproves the conjectures that all nonintegrable systems satisfy the ETH and that the ETH is a necessary condition for thermalization. I also discuss the hardness of the problem of thermalization from the viewpoint of computational science [8]. Then, I move to an analytical approach to a concrete model, and prove that S=1/2 XYZ chain with a magnetic field is nonintegrable [9]. This is the first example of proof of nonintegrability in a concrete quantum manybody system, which will help a mathematical approach to thermalization.
*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
References
 S. Popescu, A. Short, A. Winter, Nat. Phys. 2, 754 (2006)
 P. Reimann, Phys. Rev. Lett, 101, 190403 (2008)
 M. Srednicki, PRE 50, 888 (1994)
 M. Rigol, V. Dunjko & M. Olshanii, Nature 452, 854 (2008)
 T. Mori, arXiv:1609.09776 (2016)
 N. Shiraishi and T. Mori, Phys. Rev. Lett. 119, 030601 (2017)
 T. Mori and N. Shiraishi, Phys. Rev. E 96, 022153 (2017)
 N. Shiraishi and K. Matsumoto, in preparation
 N. Shiraishi, Europhys. Lett. 128, 17002 (2019)