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Туннельное возмущение дискретного спектра
С. 10-10.
Vybornyi E.
In book
М. : МИЭМ НИУ ВШЭ, 2013
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
Bruning J., Grushin V. V., Dobrokhotov S. Y., Математические заметки 2012 Т. 92 № 2 С. 163-180
An example of Schrodinger and Klein-Gordon equations with fast oscillating coefficients is used to show that they can be averaged by an adiabatic approximation based on V.P. Maslov's operator method. ...
Added: December 24, 2012
Vybornyi E., Theoretical and Mathematical Physics 2014 Vol. 178 No. 1 P. 93-114
We consider the one-dimensional stationary Schr¨odinger equation with a smooth double-well potential. We obtain a criterion for the double localization of wave functions, exponential splitting of energy levels, and the tunneling transport of a particle in an asymmetric potential and also obtain asymptotic formulas for the energy splitting that generalize the well-known formulas to the ...
Added: December 23, 2013
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
Karasev M., Vybornyi E., / Cornell University. Series "Working papers by Cornell University". 2014. No. 1411.4436.
We consider the one-dimensional Schr\"{o}dinger 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 initial state localized in the physical well. It is shown that if ...
Added: November 18, 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
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
Bruning J., Grushin V. V., Dobrokhotov S. Y., Russian Journal of Mathematical Physics 2012 Vol. 19 No. 3 P. 261-272
In the paper, using relatively simple formulas derived in the abstract perturbation theory of selfadjoint operators, we obtain explicit asymptotic formulas for a family of elliptic operators of Laplace type that arise in linear problems with rapidly oscillating coefficients. ...
Added: December 24, 2012
Anikin A. Y., Brüning J., Dobrokhotov S. et al., Russian Journal of Mathematical Physics 2019 Vol. 26 No. 3 P. 265-276
In this paper, we consider the spectral problem for the magnetic Schrödinger operator on the 2-D plane (x1, x2) with the constant magnetic field normal to this plane and with the potential V having the form of a harmonic oscillator in the direction x1 and periodic with respect to variable x2. Such a potential can ...
Added: September 18, 2019
Vybornyi E., Karasev M., Наноструктуры. Математическая физика и моделирование 2014 Т. 11 № 1 С. 27-36
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 initial state localized in the physical well. It is shown that if the probing
well ...
Added: October 23, 2014
Vybornyi E., Karasev M., Russian Journal of Mathematical Physics 2018 Vol. 25 No. 4 P. 500-508
We consider a charge in a general electromagnetic trap near a hyperbolic stationary point. The two-dimensional trap Hamiltonian is a sum of hyperbolic harmonic part and higher order anharmonic corrections. We suppose that two frequencies of the harmonic part are under a resonance 1 : (-1). In this case, anharmonic terms define the dynamics and ...
Added: November 16, 2018
Karasev M., Novikova E., Vybornyi E., Mathematical notes 2016 Vol. 100 No. 6 P. 807-819
We describe how a top-like quantum Hamiltonian over a non-Lie algebra appears in the model of the planar Penning trap under breaking its axial symmetry (inclination of the magnetic field) and turning parameters (electric voltage, magnetic field strength and inclination angle) at double resonance. For eigenvalues of the quantum non-Lie top, under a specific variation ...
Added: October 22, 2016
Baranov A., Yakubovich D., Journal of Mathematical Analysis and Applications 2015 Vol. 424 No. 2 P. 1404-1424
We study spectral properties of one-dimensional singular nonselfadjoint perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type. A counterpart of our results for
the case of bounded operators provides a complete description of compact selfadjoint operators whose rank one perturbation is a
Volterra ...
Added: March 6, 2016
Алексеева Е. С., Рассадин А. Э., Вестник Дагестанского государственного университета 2020 Т. 35 № 3 С. 7-11
Approximate conformal mapping of the exterior of the domain on phase plane restricted by phase trajectory of the weakly nonlinear oscillator on the exterior of the unit disk is calculated in the paper. The aim of this consideration is to clarify the interrelation of Hamiltonian systems on plane with discovered at the beginning of our ...
Added: December 16, 2022
Arseyev P., Mantsevich V. N., Maslova N. S., JETP Letters 2012 Vol. 95 No. 10 P. 589-594
The possibility of non-adiabatic electron pumping in the system of three coupled quantum dots attached to the leads is discussed. We have found out that periodical changing of energy level position in the middle quantum dot results in non zero mean tunneling current appeared due to non-adiabatic non-equilibrium processes. The same principle can be used ...
Added: October 28, 2014
Zlotnik A., Zlotnik I. A., Kinetic and Related Models 2012 Vol. 5 No. 3 P. 639-667
We consider the time-dependent 1D Schrödinger equation on the half-axis with variable coefficients becoming constant for large x. We study a two-level symmetric in time (i.e. the Crank-Nicolson) and any order finite element in space numerical method to solve it. The method is coupled to an approximate transparent boundary condition (TBC). We prove uniform in ...
Added: March 21, 2013
Pereskokov A., Липская А. В., Вестник Московского энергетического института 2010 № 6 С. 99-109
Рассмотрены радиально-симметричные решения уравнения типа Хартри, содержащего как кулоновский потенциал, так и интегральную нелинейность с потенциалом взаимодействия Юкавы. В квазиклассическом приближении выведены и исследованы уравнения для самосогласованного потенциала. Выписано правило квантования типа Бора-Зоммерфельда. Найдены асимптотические собственные значения и собственные функции. ...
Added: December 16, 2012
Ducomet B., Zlotnik A., Romanova A. V., / Cornell University. Series math "arxiv.org". 2013. No. 1309.7280.
An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schrödinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we first construct higher order scheme with splitting space averages having much better spectral properties for $n\geq 3$. Next we apply the Strang-type splitting with respect to the potential ...
Added: October 1, 2013
Karasev M., Russian Journal of Mathematical Physics 2012 Vol. 19 No. 3 P. 299-306
For the Dirac 2D-operator in a constant magnetic field with perturbing electric potential, we derive Hamiltonians describing the quantum quasiparticles (Larmor vortices) at Landau levels. The discrete spectrum of this Hall-effect quantum Hamiltonian can be computed to all orders of the semiclassical approximation by a deformed Planck-type quantization condition on the 2D-plane; the standard magnetic (symplectic) ...
Added: December 19, 2012
Zlotnik A., Romanova A. V., / Cornell University. Series math "arxiv.org". 2013. No. arxiv: 1307.5398.
We consider an initial-boundary value problem for a 2D time-dependent Schrödinger equation on a semi-infinite strip. For the Numerov-Crank-Nicolson finite-difference scheme with discrete transparent boundary conditions, the Strang-type splitting with respect to the potential is applied. For the resulting method, the uniqueness of a solution and the uniform in time L_2-stability (in particular, L_2-conservativeness) are ...
Added: July 24, 2013
Galkin O., Galkina S., / Cornell University. Series math "arxiv.org". 2020. No. arXiv:2012.07174.
This short communication (preprint) is devoted to mathematical study of evolution equations that are important for mathematical physics and quantum theory; we present new explicit formulas for solutions of these equations and discuss their properties. The results are given without proofs but the proofs will appear in the longer text which is now under preparation.
In ...
Added: December 13, 2020
Chetverikov V., Mamsurov I., , in : Proceedings of 2022 IEEE Moscow Workshop on Electronic and Networking Technologies (MWENT). : M. : IEEE, 2022. P. 1-4.
The solutions of the Schrodinger (Schrodinger – Pauli) equations and the Dirac equation in the 2+1 space for the two-dimensional motion of a charged particle in a uniform and constant magnetic field, as well as the construction of coherent states based on the solutions obtained are considered. A specific feature of this problem is the ...
Added: October 25, 2022
Arbuzov A., Bardin D., Bondarenko S. et al., JETP Letters 2016 Vol. 103 No. 2 P. 131-136
This article presents new features of the MCSANC v.1.20 program, a Monte Carlo tool for calculation of the next-to-leading order electroweak and QCD corrections to various Standard Model processes. The extensions concern implementation of Drell--Yan-like processes and include a systematic treatment of the photon-induced contribution in proton--proton collisions and electroweak corrections beyond NLO approximation. There ...
Added: June 28, 2018