Mathematics of thermalization in isolated quantum systems
- 2020年11月10日16:00 - 18:10 (JST)
- 白石 直人 (学習院大学 理学部 物理学科 助教) Edit
- via Zoom
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 many-body systems thermalize, while some many-body 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 long-standing 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 , relaxation caused by large effective dimension , and eigenstate thermalization hypothesis (ETH) [3,4] and weak-ETH .
In the second part of my talk, I explain some of my results. First, I introduce a model which is non-integrable 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 . 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 . This is the first example of proof of nonintegrability in a concrete quantum many-body system, which will help a mathematical approach to thermalization.
*Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
- 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)