Theory and application of mathematical analysis on 1D Bose systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540399
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Shizuoka University
• Principal Investigator: Suzuki Junji 静岡大学, 理学部, 教授 (40222062)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 量子相関 / 可積分系 / 量子転送行列法 / 厳密WKB法 / フレッドホルム行列

Outline of Final Research Achievements

We have developed an analytic framework to deal with mathematical problems arising from the quantum correlations in one dimensional Bose system and related models of finite and infinite size. It combines the method of quantum transfer matrix and the exact WKB method. We have obtained exact, concrete and quantitative results in various physical systems. In particular we have analyzed correlation functions in higher spin chains which reduces to the Bose system in a scaling limit. Then a hidden link between this physical system and the Riemann's zeta function has been found. We also analyzed the so called thermodynamic Bethe ansatz for the wider class of supersymmetric systems
which generalizes the Bose system. We have found analytic solutions to these equations for the first time. By applying this machinery, we predict theoretically the existence of three different time regimes in the dynamics of anisotropic Heisenberg spin chains.

Free Research Field

統計力学