# iTHEMS math-phys Working Group

iTHEMS Mathematical Physics Working Group (November 1st 2021-).

The purpose of iTHEMS math-phys Working Group is to carry out research in mathematical physics in close cooperation between mathematicians and physicists.

## Objecties

Mathematics and physics have been keeping a close connection from the time of their birth. However, their relationship is becoming a little less effective compared with the old days due to different characters between modern mathematics and physics. The purpose of the math-phys working group is to restore their close relationship and to enhance the interaction for the purpose of the integrated development of mathematical physics.

To have efficient discussions and collaborations, we plan to organize our activity by focussing on the following two topics:

### A. Mathematical physics of macroscopic properties of many-body systems

It has been one of the most important problems in theoretical physics to understand macroscopic properties (e.g., thermodynamic and transport properties) from underlying microscopic models. Correspondingly, there are fruitful research areas in mathematics, such as probability theory, topology, and group theory. While there are various computational techniques in theoretical physics (such as the density functional theory in atomic physics), less is known about their mathematical foundation and the regime of applicability. In order to develop a clearer understanding of mathematical aspects of many-body systems, it is strongly desirable to share interesting models, methods, and mathematical bases between mathematics and physics. To accomplish this, we are planning to work on (A-1) thermodynamic properties of many-body systems and their relations to mathematical concepts like the large deviation theory and integrability, etc., (A-2) transport phenomena and hydrodynamic limit, and (A-3) relation between lattice models and effective field theories.

### B. Mathematical physics of Schrödinger-type equation

The Schrödinger-type equation appears in diverse areas of theoretical physics, from quantum mechanics and hydrodynamics to black hole physics. While the scattering theory gives a rigorous theoretical framework to describe the Schrödinger-type equation, there are also different descriptions relying on, e.g., the path-integral formalism of quantum theory (and stochastic process). To establish the unified view on the diverse phenomena and theoretical formulations, we will work on (B-1) Scattering theory of Schrödinger-type equation, (B-2) Nonperturbative methods such as the resurgence theory and exact WKB analysis, and (B-3) Tunnelling-like phenomena with the help of the real-time path integral.

- Facilitators:
- Masaru Hongo (UIC) *Contact at masaru.hongo@a.riken.jp
- Ryo Namba (RIKEN iTHEMS)
- Makiko Sasada (Univ. Tokyo)
- Hiroyasu Miyazaki (RIKEN iTHEMS)
- Yukimi Goto (RIKEN iTHEMS)
- Keita Mikami (RIKEN iTHEMS)