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## Averaging and spectral bands for 2-D magnetic Schrödinger operator with the growing and one-direction periodic potential

Russian Journal of Mathematical Physics. 2019. Vol. 26. No. 3. P. 265-276.

Anikin A. Y., Brüning J., Dobrokhotov S., Vybornyi E.

In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (*x*1*, x*2) with the constant magnetic field normal to this plane and with the potential *V *having the form of a harmonic oscillator in the direction *x*1 and periodic with respect to variable *x*2. Such a potential can be used for modeling a long molecule. We assume that the magnetic field is quite large, this allows us to make the averaging and to reduce the original problem to a spectral problem for a 1-D Schrödinger operator with effective periodic potential. Then we use semiclassical analysis to construct the band spectrum of this reduced operator, as well as that of the original 2-D magnetic Schrödinger operator.

Priority areas:
mathematics

Language:
English

Publication based on the results of:

Chernyshev V.L., Russian Journal of Mathematical Physics 2016 Vol. 23 No. 3 P. 348-354

On a two-dimensional surface, a Schrödinger operator is considered with a potential whose critical points form a closed curve. We pose the problem of describing the semiclassical spectral series corresponding to this curve. The standard construction for describing the spectral series corresponding to isolated nondegenerate equilibria or to periodic trajectories of Hamiltonian systems is not ...

Added: October 25, 2014

Karasev M., Vybornyi E., Journal of Mathematical Physics 2016

We consider the one-dimensional Schrodinger operator in the semiclassical regime assuming that its double-well potential is the sum of a finite "physically given" well and a square shape probing well whose width or depth can be varied (tuned). We study the dynamics of an initial state localized in the physical well. It is shown that ...

Added: October 23, 2015

Vybornyi E., Наноструктуры. Математическая физика и моделирование 2015 Т. 13 № 2 С. 43-54

We conceder semiclassical asymptotics of the energy levels shift of the Schrödinger operator discrete spectrum with a one-dimensional single-well potential that appears due to a deformation of the potential in the classically forbidden region. Since such a deformation of the potential effects on the quantum particle only due to the tunneling effects, then the corresponding ...

Added: February 18, 2016

Vybornyi E., Наноструктуры. Математическая физика и моделирование 2015 Т. 12 № 1 С. 5-84

We consider the problem of constructing semiclassical asymptotic expansions of discrete spectrum and the corresponding stationary states of one-dimensional Schrödinger operator in the case of resonance tunneling. We consider two basic models: tunneling in an asymmetric double-well potential on a line and momentum tunneling of a particle in a potential field on a circle. For ...

Added: February 12, 2016

Vybornyi E., Theoretical and Mathematical Physics 2014 Vol. 181 No. 2 P. 1418-1427

We propose an operator method for calculating the semiclassical asymptotic form of the energy splitting value in the general case of tunneling between symmetric orbits in the phase space. We use this approach in the case of a particle on a circle to obtain the asymptotic form of the energy tunneling splitting related to the ...

Added: August 5, 2014

BOSSY M., Jabir J. M., Electronic Communications in Probability 2018 Vol. 23 P. 1-14

In this paper, we prove a particle approximation, in the sense of the propagation of chaos, of a Lagrangian stochastic model submitted to specular boundary condition and satisfying the mean no-permeability condition. ...

Added: June 7, 2018

Belavin V., Geiko R., Journal of High Energy Physics 2017 Vol. 125 P. 1-13

We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS3/CFT2 correspondence. To give such an interpretation in previous studies, certain restrictions were necessary. Our goal here is to consider a more general situation available through the worldline approximation to the dual AdS gravity. ...

Added: August 31, 2017

Akhmedov E., Physical Review D - Particles, Fields, Gravitation and Cosmology 2013 Vol. 87 No. 4 P. 044049

Following Krotov and Polyakov [ Nucl. Phys. B849 410 (2011)], we show that in global de Sitter space its isometry is broken by the loop IR divergences for any invariant vacuum state of the massive scalars. We derive a kinetic equation in global de Sitter space that follows from the Dyson-Schwinger equation of the Schwinger-Keldysh ...

Added: February 27, 2013

Kurkina O. E., Kurkin A. A., Rouvinskaya E. et al., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 95 № 2 С. 98-103

Nonlinear wave dynamics is discussed using the extended modified Korteweg–de Vries equation that includes the combination of the third- and fifth- order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are ...

Added: August 24, 2012

Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416-432

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...

Added: November 19, 2014

Зайцев В. И., Щавелин В. М., М. : ВИНИТИ РАН, 1985

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Arseyev P., Mantsevich V. N., Maslova N. S., JETP Letters 2011 Vol. 94 No. 5 P. 422-428

We present theoretical investigation of spatial charge distribution in the two-level system with strong Coulomb correlations by means of Heisenberg equations analysis for localized states total electron filling numbers taking into account pair correlations of local electron density. It was found that tunneling current through nanometer scale structure with strongly coupled localized states causes Coulomb ...

Added: October 28, 2014

Пенза : ПГУ, 2015

В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...

Added: May 31, 2015

Буров А.А., Герман А. Д., Косенко И. И., Космические исследования 2014 Т. 52 № 4 С. 307-312

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We ...

Added: November 8, 2014

Aseeva N., Gromov E., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 653-657

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is well known as a part of the temporal domain NLSE in optics. In this context, it is induced by the ...

Added: June 28, 2016

Семин С. В., Kurkina O. E., Kurkin A. A. et al., Труды НГТУ им. Р.Е. Алексеева 2012 № 2(95) С. 48-65

Purpose: Numerical modeling of internal baroclinic disturbances of different shapes in a model lake with variable depth, analysis of velocity field of wave-induced current, especially in the near-bed layer.
Approach: The study is carried out with the use of numerical full nonlinear nonhydrostatic model for stratified fluid.
Findings: The full nonlinear numerical modeling of internal wave dynamics ...

Added: October 6, 2012

Florido Calvo F. A., Remizov I., / Cornell University. Series arXiv "math". 2021.

Dynamics of closed quantum systems on curves, surfaces and more general manifolds is governed by the Schroedinger equation with time-independent Hamiltonian. Solving Cauchy problem for this equation provides full information on the future and the past of the system if we know the state of the system at the initial moment of time t=0. However, ...

Added: December 16, 2021

Zhuzhoma E. V., Medvedev V., Исаенкова Н. В., Нелинейная динамика 2017 Т. 13 № 3 С. 399-412

В статье, используя методы теории динамических систем Морса–Смейла, авторы рассматривают топологическую структуру для точечно-зарядной модели магнитного поля областей фотосферы. Для произвольного количества зарядов (безотносительно к их местоположению) и не предполагая потенциальности поля <span data-mathml="B⃗ (следовательно, не используя конкретных формул), авторы приводят оценки, связывающие количества зарядов определенного типа с количеством нуль-точек. Для граничных оценок описывается топологическая структура магнитного ...

Added: October 12, 2017

49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168-173

The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...

Added: August 25, 2019

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1-8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

Budkov Y., Journal of Physics: Condensed Matter 2019 Vol. 31 P. 078002-078003

We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001). ...

Added: January 4, 2019

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Musaev E., Berman D. S., Thompson D. C., Journal of High Energy Physics 2012 Vol. 1210

The reduction of the duality invariant approach to M-theory by a U-duality group valued
Scherk-Schwarz twist is considered. We show that all gaugings of SUGRA can be obtained
by dimensional reduction of the extended space. ...

Added: October 20, 2014