MATSUI Chihiro
Title

Associate Professor 
Field

Mathematical physics 
Research interests

Quantum solvable models, Solvable stochastic processes 
Current research

My main research interest is quantum solvable models. Although no clear definition is given for quantum solvable models, here we say a system is solvable when manybody scatterings are decomposed into a sequence of twobody scatterings. The decomposability of manybody scatterings into twobody ones is guaranteed by the YangBaxter equation. The YangBaxter equation is understood in the context of algebra such as quantum groups, and thus allows us to derive exact physical quantities through the algebraic relations. The famous example is the spin1/2 Heisenberg chain with anisotropy called the XXZ chain. A Scattering process of a quantum field theory (QFT) is described by the transfer matrix of the corresponding spin chain. This is achieved by considering the discretization of the light cone, called the lightcone lattice regularization. The XXZ model is a nonsupersymmetric model, while its extension to the higherspin cases allows us to obtain the supersymmetry in their corresponding QFTs. The aim of my research is to explore how the supersymmetry arises in the corresponding QFTs to the nonsupersymmetry spin chains from the viewpoint of characteristic degrees of freedom in the higherspin cases. Another topic of my research interest is solvable stochastic processes. The asymmetric simple exclusion process (ASEP) is a onedimensional stochastic process with discrete space and continuum time. This model obeys a master equation with a Markov matrix, which satisfies the TemperleyLieb algebra, and thus leads to solvability of the system in the sense that the steady states are exactly derived. Due to the nice mathematical structure of the Markov matrix, various algebraic extensions of the ASEP can be considered. The multistate extension, which allows more than one particle to occupy the same site, is achieved by considering the higherdimensional representation of the TemperleyLieb algebra. This model describes multiple particles hopping at the same time on one dimension and, therefore, is applicable to micromeritics and traffic engineering. 
Selected publications


Memberships, activities and Awards 
The Physical Society of Japan The Mathematical Society of Japan 2017 Journal editorial board of the membership journal of The Physical Society of Japan 