# Mathematics of thermalization in isolated quantum systems

- Date
- November 10 at 16:00 - 18:10, 2020 (JST)

- Speaker
- Dr. 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 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 [1], relaxation caused by large effective dimension [2], and eigenstate thermalization hypothesis (ETH) [3,4] and weak-ETH [5].

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 [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 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.

## References

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- 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)