Exact quantum dynamics of yrast states in the finite 1D Bose gas

22nd International Laser Physics Workshop

Kaminishi, Eriko^1 ; Sato, Jun^2 ; Deguchi, Tetsuo^2

Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan^1

Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan^2

关键词: Canonical ensemble;    Dynamical relaxation;    Expectation values;    Finite-size corrections;    Local operators;    Localized state;    Quantum dynamics;    Quantum many-body systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/497/1/012030/pdf
DOI  :  10.1088/1742-6596/497/1/012030

来源: IOP

【 摘 要 】

We demonstrate that the quantum dynamics of yrast states in the one-dimensional (1D) Bose gas gives an illustrative example to equilibration of an isolated quantum many-body system. We first formulate the energy spectrum of yrast states in terms of the dressed energy by applying the method of finite-size corrections. We then review the exact time evolution of quantum states constructed from yrast states shown by the Bethe ansatz. In time evolution the density profile of an initially localized quantum state constructed from yrast states collapses into a flat profile in the case of a large particle number such as N 1000, while recurrence of the localized state occurs in the case of a small particle number such as N 20. We suggest that the dynamical relaxation behavior for the large N case is consistent with the viewpoint of typicality for generic quantum states: the expectation values of local operators evaluated in most of quantum states are very close to those of the micro-canonical ensemble.