Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation

• URL: http://arxiv.org/abs/2207.00293v3
• Date: Fri, 7 Apr 2023 09:33:15 GMT
• Title: Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation
• Authors: Kayo Kinjo, Jun Sato, Tetsuo Deguchi
• Abstract summary: We show novel aspects in the exact non-equilibrium dynamics of quantum double dark-soliton states in the Lieb-Liniger model. It is suggested that the quasi-BEC should play a significant role in the dynamics of quantum double dark-soliton states.
• Score: 4.176752121302987
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show several novel aspects in the exact non-equilibrium dynamics of quantum double dark-soliton states in the Lieb-Liniger model for the one-dimensional Bose gas with repulsive interactions. We also show an exact finite-size scaling of the fraction of the Bose-Einstein condensation (BEC) in the ground state, which should characterize the quasi-BEC in quantum double dark-soliton states that we assume to occur in the weak coupling regime. First, we show the exact time evolution of the density profile in the quantum state associated with a quantum double dark-soliton by the Bethe ansatz. Secondly, we derive a kind of macroscopic quantum wave-function effectively by exactly evaluating the square amplitude and phase profiles of the matrix element of the field operator between the quantum double dark-soliton states. The profiles are close to those of dark-solitons particularly in the weak-coupling regime. Then, the scattering of two notches in the quantum double dark-soliton state is exactly demonstrated. It is suggested from the above observations that the quasi-BEC should play a significant role in the dynamics of quantum double dark-soliton states. If the condensate fraction is close to 1, the quantum state should be well approximated by the quasi-BEC state where the mean-field picture is valid.

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