Semi-classical analysis with new Galilean transformations for a Gross--Pitaevskii system with non-zero conditions at infinity
Abstract
Recently, a rich variety of the micro-phenomena of the superfluid passing an obstacle has been observed in the binary mixture of rotating Bose--Einstein condensates (BECs). Among such phenomena, the interaction of dark--bright solitons is one of the most important issues. In this work we investigate the semi-classical limit for a coupled system of Gross--Pitaevskii (GP) equations with rotating fields and trap potentials in a two-dimensional exterior domain, where the superfluid is non-vanishing at infinity. We establish a new Galilean type transformation and follow the argument of the modulated energy functional (a Lyapunov type functional) in \cite{ll08,lz05} to control the propagation of mass densities and linear momenta of the solution via a compressible Euler equation with Coriolis force in a semi-classical regime. Moreover, the effect of the rotating field on the superfluid in the region far away from the obstacle is precisely described.
Keywords
Cite
@article{arxiv.1904.04739,
title = {Semi-classical analysis with new Galilean transformations for a Gross--Pitaevskii system with non-zero conditions at infinity},
author = {Qi Gao and Chiun-Chang Lee and Tai-Chia Lin},
journal= {arXiv preprint arXiv:1904.04739},
year = {2019}
}