Tetrahedron equation and quantum integrable systems

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K04892
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Kuniba Atsuo 東京大学, 大学院総合文化研究科, 教授 (70211886)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 可積分系 / マルコフ過程 / 量子群 / ヤン・バクスター方程式 / 四面体方程式 / 行列積

Outline of Final Research Achievements

An integrable model in Markov processes in non-equilibrium statistical mechanics was constructed. It is formulated as a stochastic dynamics of n kinds of particles on one-dimensional lattice obeying asymmetric transition rules. It includes a majority of such models which have been studied so far. The relation to the tetrahedron equation and the theory of crystal base of quantum groups was clarified and a matrix product formula was derived for the stationary states. They revealed the representation theoretical origin of the known algorithm to calculate stationary probabilities.
For n=2, density and current profile of the particles were derived and the physical aspects of the model was clarified both qualitatively and quantitatively.

Free Research Field

数理物理学