Aspects in the non-equilibrium dynamics of integrable quantum systems: quantum quench and exact solutions of the Kondo problem

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K05204
• 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, 基幹研究院, 教授 (70227544)
• Co-Investigator(Renkei-kenkyūsha): SATO JUN 東京大学, 先端科学技術研究センター, 助教 (10735723) ; KUDO KAZUE お茶の水女子大学, 基幹研究院, 准教授 (30505574)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 可積分量子系 / 孤立量子系 / 量子ダイナミクス / ベーテ仮設 / ダークソリトン / 非平衡 / 量子多体系

Outline of Final Research Achievements

Recently, relaxation behaviors of isolated quantum systems were observed in cold atomic experiments. It is conjecture that in non-integrable systems expectation values of localized physical quantities approach values associated with the micro-canonical ensemble (thermalization), while in integrable systems values associated with the generalized Gibbs ensemble. In this research we studied aspects of non-equilibrium dynamics for integrable systems. For the one-dimensional Bose gas (the Lieb-Liniger model), some superposition of one-hole states shows a density profile consistent with a classical dark soliton in the weak coupling case. We call it a quantum dark soliton state. In the one-dimensional Heisenberg model we constructed a quantum state that has a localized magnetization profile, and derived its time evolution with the Bethe ansatz. We have observed that it relaxes very slowly almost proportional to some power of time variable.

Free Research Field

数理物理学