Math-Phys Seminar
23 events
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Seminar
Mathematics of thermalization in isolated quantum systems
November 10 (Tue) 16:00 - 18:10, 2020
Naoto Shiraishi (Assistant Professor, Department of Physics, Faculty of Science, Gakushuin University)
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.
Venue: via Zoom
Event Official Language: English
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Seminar
TQFT, integrable lattice model, and quiver gauge theories
October 2 (Fri) 16:00 - 18:00, 2020
Toshihiro Ota (Student Trainee, RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) / Ph.D. Student, Graduate School of Science, Osaka University)
1st part (math): In physics literature, “lattice models” appear quite often as mathematical models of physical systems, e.g. Ising model, vertex models, lattice gauge theory. The aim of the 1st part is to introduce ‘what is (T)QFT,’ ‘what is lattice model,’ and ‘what does integrability mean’ in the language of mathematics. In turn, they will play a crucial role in the 2nd part of my talk. I also hope that this will lead to a good exchange among us, especially between physicists and mathematicians. 2nd part (physics): In the 2nd part, I would like to explain where an integrable lattice model may come from, especially for people in the physics background. I will show a certain class of integrable lattice models is realized by Wilson-’t Hooft lines in 4d quiver gauge theories. I will also explain a bit how these gauge theories are constructed from brane configurations in string theory. String dualities allow us to relate the original 4d setups to 4d partially topological Chern-Simons theory, which is a partial TQFT and generates integrable lattice models. Please contact Keita Mikami's mail address to get access to the Zoom meeting room.
Venue: via Zoom
Event Official Language: English
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Seminar
Geometric Perspective for the Theory of Hydrodynamic Limits
August 31 (Mon) - September 1 (Tue) 2020
Makiko Sasada
Kenichi Bannai (Professor, Faculty of Science and Technology Department of Mathematics, Keio University)This is a series of lectures on "Geometric Perspectives for Fluid Dynamic Limit Theory" by the following speakers: [DAY 1: Aug 31] Dr. Makiko Sasada (University of Tokyo) [DAY 2: Sept 1] Prof. Kenichi Bannai (Keio University) Abstract: One of the fundamental problems in the natural and social sciences is to explain macroscopic phenomena that we can observe from the rules governing the microscopic system giving rise to the phenomena. Hydrodynamic limit provides a rigorous mathematical method to derive the deterministic partial differential equations describing the time evolution of macroscopic parameters, from the stochastic dynamics of a microscopic large scale interacting system. In the article "Topological Structures of Large Scale Interacting Systems via Uniform Locality" joint with Yukio Kametani, we introduce a general framework encompassing a wide variety of interacting systems in order to systematically investigate various microscopic stochastic large scale interacting systems in a unified fashion. In particular, we introduced a new cohomology theory called the uniformly local cohomology to investigate the underlying geometry of the interacting system. Our theory gives a new interpretation of the macroscopic parameters, the role played by the group action on the microscopic system, and the origin of the diffusion matrix associated to the macroscopic deterministic partial differential equation obtained via the space-time scaling limit of the microscopic system. The purpose of the series of lectures is to introduce to the audience the theory of hydrodynamic limits, especially the relation between the macroscopic observables and the microscopic interacting system. We then explain our new perspective of how geometry comes into play in investigating the interacting system, and introduce the ideas and results of our article. *Detailed information about the seminar refer to the email.
Venue: via Zoom
Event Official Language: English
23 events