Abstract
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.
Highlights
Ultracold quantum gases have attracted much interest due to their potential application to the testing of the quantum fluctuations in many-body systems [1, 2, 3, 4]
In the Gross-Pitaevskii mean-field picture, if the angular momentum is given by an integral multiple of the number of particles, N, the vortex core is located on the rotating axis, while if not, it is not [18]
The main purpose of the present report is to review interesting dynamical properties in the quantum dynamics associated with yrast states in the 1D Bose gas [50]
Summary
Ultracold quantum gases have attracted much interest due to their potential application to the testing of the quantum fluctuations in many-body systems [1, 2, 3, 4]. In quantum many-body systems such as rotating nuclei, it is often important to study such eigenstates that have the lowest energy among all the eigenstates with the same given angular momentum [15]. It is an interesting problem to study many-body phenomena in the 1D Bose gas theoretically and to compare the theoretical results with experimental ones It is one of the greatest achievements in exactly solvable models that finite-temperature specific heat and magnetic susceptibility are explicitly evaluated by the Bethe-ansatz method [37, 38, 39]. The main purpose of the present report is to review interesting dynamical properties in the quantum dynamics associated with yrast states in the 1D Bose gas [50].
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