| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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.
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