https://doi.org/10.1140/epjp/s13360-025-06183-6
Regular Article
Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation
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
4
Laboratory for Theoretical Cosmology, International Centre of Gravity and Cosmos, Tomsk State University of Control Systems and Radioelectronics, 40 Lenina av., 634050, Tomsk, Russia
Received:
23
September
2024
Accepted:
2
March
2025
Published online:
21
March
2025
We deal with the n-dimensional nonlinear Schrödinger equation (NLSE) with a cubic nonlocal nonlinearity and an anti-Hermitian term, which is widely used model for the study of open quantum system. We construct asymptotic solutions to the Cauchy problem for such equation within the formalism of semiclassical approximation based on the Maslov complex germ method. Our solutions are localized in the neighbourhood of a few points for every given time, i.e. form some spatial pattern. The localization points move over trajectories that are associated with the dynamics of semiclassical quasiparticles. The Cauchy problem for the original NLSE is reduced to the system of ordinary differential equations and auxiliary linear equations. The semiclassical nonlinear evolution operator is derived for the NLSE. The general formalism is applied to the specific one-dimensional and two-dimensional NLSEs with a periodic trap potential, dipole-dipole interaction, and phenomenological damping. It is shown that the long-range interactions in such model, which are considered through the interaction of quasiparticles in our approach, can lead to drastic changes in the behaviour of our asymptotic solutions.
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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.
