The Gross-Pitaevskii Equation with a Nonlocal Interaction in a Semiclassical Approximation on a Curve

被引：6

作者：

Shapovalov, Alexander V. ^{[1
,2
]}

Kulagin, Anton E. ^{[3
,4
]}

Trifonov, Andrey Yu. ^{[2
,3
]}

机构：

[1] Tomsk State Univ, Dept Theoret Phys, 1 Novosobornaya Sq, Tomsk 634050, Russia

[2] Tomsk State Pedag Univ, Dept Phys & Math, 60 Kievskaya St, Tomsk 634041, Russia

[3] Tomsk Polytech Univ, Dept Math & Informat, 30 Lenin A, Tomsk 634050, Russia

[4] Russian Acad Sci, Siberian Branch, VE Zuev Inst Atmospher Opt, 1 Academician Zuev Sq, Tomsk 634055, Russia

来源：

SYMMETRY-BASEL | 2020年 / 12卷 / 02期

关键词：

Gross-Pitaevskii equation; nonlocal interaction; Bose-Einstein condensate; semiclassical approximation; complex germ; symmetry operators; BOSE-EINSTEIN CONDENSATION; ASYMPTOTICS;

D O I：

10.3390/sym12020201

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross-Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (curve) that evolves over time. The approach reduces the Cauchy problem for the nonlocal Gross-Pitaevskii equation to a similar problem for the associated linear equation. The geometric properties of the resulting solutions are related to Maslov's complex germ, and the symmetry operators of the associated linear equation lead to the approximation of the symmetry operators for the nonlocal Gross-Pitaevskii equation.

引用

页数：25

共 56 条

[1] Born-Infeld condensate as a possible origin of neutrino masses anddark energy [J].

Addazi, Andrea ;

Capozziello, Salvatore ;

Odintsov, Sergei .

PHYSICS LETTERS B, 2016, 760 :611-616

[2]

Babic V.M., 1972, Short-wavelength diffraction theory

[3] Semiclassical trajectory-coherent approximation in quantum mechanics .1. High-order corrections to multidimensional time-dependent equations of schrodinger type [J].

Bagrov, VG ;

Belov, VV ;

Trifonov, AY .

ANNALS OF PHYSICS, 1996, 246 (02) :231-290

[4] Theoretical progress in many-body physics with ultracold dipolar gases [J].

Baranov, M. A. .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2008, 464 (03) :71-111

[5] All-optical production of chromium Bose-Einstein condensates [J].

Beaufils, Q. ;

Chicireanu, R. ;

Zanon, T. ;

Laburthe-Tolra, B. ;

Marechal, E. ;

Vernac, L. ;

Keller, J. -C. ;

Gorceix, O. .

PHYSICAL REVIEW A, 2008, 77 (06)

[6] Bose-Einstein condensation in large time-averaged optical ring potentials [J].

Bell, Thomas A. ;

Glidden, Jake A. P. ;

Humbert, Leif ;

Bromley, Michael W. J. ;

Haine, Simon A. ;

Davis, Matthew J. ;

Neely, Tyler W. ;

Baker, Mark A. ;

Rubinsztein-Dunlop, Halina .

NEW JOURNAL OF PHYSICS, 2016, 18

[7] Semiclassical trajectory-coherent approximations of Hartree-type equations [J].

Belov, VV ;

Trifonov, AY ;

Shapovalov, AV .

THEORETICAL AND MATHEMATICAL PHYSICS, 2002, 130 (03) :391-418

[8] SEMICLASSICAL MASLOV ASYMPTOTICS WITH COMPLEX PHASES .1. GENERAL-APPROACH [J].

BELOV, VV ;

DOBROKHOTOV, SY .

THEORETICAL AND MATHEMATICAL PHYSICS, 1992, 92 (02) :843-868

[9]

Belov VV., 2002, International Journal of Mathematics and Mathematical Sciences, V32, P325

[10] Superfluidity of dipolar excitons in a transition metal dichalcogenide double layer [J].

Berman, Oleg L. ;

Kezerashvili, Roman Ya. .

PHYSICAL REVIEW B, 2017, 96 (09)

← 1 2 3 4 5 6 →