https://doi.org/10.1140/epjp/s13360-025-07236-6
Regular Article
Semiclassical states localized on a one-dimensional manifold and governed by the nonlocal NLSE with an anti-Hermitian term
1
Tomsk Polytechnic University, 30 Lenina av., 634050, Tomsk, Russia
2
Laboratory of Quantum Electronics, V.E. Zuev Institute of Atmospheric Optics, 1 Academician Zuev Sq., 634055, Tomsk, Russia
3
Department of Theoretical Physics, Tomsk State University, Novosobornaya Sq. 1, 634050, Tomsk, Russia
Received:
9
October
2025
Accepted:
18
December
2025
Published online:
7
January
2026
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 behavior of this state is largely determined by the geometry of the localization curve.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
