2014 Fiscal Year Final Research Report

Non-equilibrium dynamics of integrable quantum many-body systems and their correlation functions: exact study of recurrence and quantum ergodicity

Research Project

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Project/Area Number	24540396
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	Ochanomizu University
Principal Investigator	DEGUCHI Tetsuo お茶の水女子大学, 大学院人間文化創成科学研究科, 教授 (70227544)
Co-Investigator(Renkei-kenkyūsha)	KUDO Kazue お茶の水女子大学, 大学院人間文化創成科学研究科, 准教授 (30505574)
Research Collaborator	SATO Jun 東京大学, 先端科学技術研究センター, 助教 (10735723) KAMINISHI Eriko 東京大学, 大学院理学研究科, PD研究員 YAHAGI Ryoko お茶の水女子大学, 大学院人間文化創成科学研究科 GIRI Pulak Ranjan お茶の水女子大学, 大学院人間文化創成科学研究科, 日本学術振興会外国人特別研究員 HATAKEYAMA Ryoko 東京大学, 大学院理学系研究科
Project Period (FY)	2012-04-01 – 2015-03-31
Keywords	可積分量子系 / 量子多体系 / 量子統計力学 / 量子ダイナミクス / 非平衡 / 典型性 / 量子ハイゼンベルグ鎖 / 代数的ベーテ仮設
Outline of Final Research Achievements	Non-equilibrium dynamics of isolated quantum many-body systems has recently attracted much attention. Collective oscillation of bunches of bosons was observed in the one-dimensional (1D) isolated quantum many-body systems of bosons thanks to the development of cold atomic experiments in the last decade. In the present research, we have studied how thermalization or more precisely equilibration occurs and shown recurrence phenomena in the dynamics of the 1D Bose gas with repulsive delta-function interaction. We also studied equilibration in the 1D quantum Heisenberg model, i.e., the XXX spin chain. For the 1D Bose gas, we constructed a quantum state with a localized density profile very close to that of a dark soliton of the GP equation, by superposing one-hole excitations. For the XXX spin chain, we derived some features of string solutions for the Bethe-ansatz equations. Furthermore, we obtained an exact solution for the XXZ spin chain with an impurity and evaluated its Wilson ratio.
Free Research Field	数理物理学