Title
"Recurrence time of a localized many-body state dynamics in the 1D Bose gas"
Eriko Kaminishi (The University of Tokyo)
Abstract
The quantum dynamics of interacting particles has recently attracted much interest associated with the question of “equilibration” and “thermalization” of isolated systems. In Ref. [1] the exact relaxation dynamics of a localized many-body state in the 1D Bose gas has been shown explicitly through the Bethe-ansatz method. Here, the localized many-body state gives a localized density profile which is the same with that of a dark soliton in the Gross-Pitaevskii equation. In our study, we calculate the dynamics of a quantum soliton exactly and observe the localized state collapsing into a flat profile in equilibrium for a large number of particles. Furthermore, we show a recurrence phenomenon for a small number of particles. In this presentation, we show that the recurrence time of the quantum integrable model is proportional to the square of the number of particles N in free-bosonic and free-fermionic regimes with small number of particles such as N =30 or 150. Furthermore, we prove analytically that the recurrence time is derived from the greatest common divisor of the energy spectra for hole excitation states in free-bosonic and free-fermionic regimes. We also numerically show the variable behavior of the time evolution of the fidelity when particles are interacting with finite value of coupling constant c which is not very small or very large.
