Semiclassical states localized on a one-dimensional manifold and governed by the nonlocal NLSE with an anti-Hermitian term

Abstract

We develop the method for constructing solutions to the nonlocal nonlinear Schrödinger equation (NLSE) with an anti-Hermitian term that are semiclassically localized on a one-dimensional manifold (a curve). The evolution of the curve is given by the closed system of integro-differential equations that can be treated as the "classical"\, analog of the open quantum system with the nontrivial geometry. Using our approach, we consider the evolution of vortex states in the open quantum system described by the specific model NLSE. The semiclassical stage of the vortex evolution can be treated as a quasi-steady vortex state. We show that the behaviour of this state is largely determined by the geometry of the localization curve.

31 pages, 3 figures

References in corpus (7)

• Observation of vortices and vortex stripes in a dipolar Bose-Einstein condensate
• Relative dynamics of quantum vortices and massive cores in binary BECs
• Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate
• Classification of the non-null electrovacuum solution of Einstein-Maxwell equations with three-parameter abelian group of motions
• Nonlocal field theory of quasiparticle scattering in dipolar Bose-Einstein condensates
• Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions
• Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation