Overexcitation of modes in an anisotropic earth-ionosphere waveguide on transequatorial paths in the presence of two close degeneracy points

Perel, M. V.

doi:10.1007/bf01039228

Cited by 10 publications

(17 citation statements)

References 2 publications

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“…Adiabatic modes, generally speaking, differ on both sides of the point x = 0 and the subscript ± indicates the side, where the mode is constructed. We note that the leading term ( 14) depends on non-perturbed eigenfunctions ϕ j , see (10), and perturbed eigenvalues βj . The Γ -normalization factor N j (x) and the diagonal conversion coefficient S jj (x) are defined as…”

Section: B Main Resultsmentioning

confidence: 99%

“…At first time, the equation ( 6) was applied to an anisotropic electromagnetic waveguide in the monography [9], where the operator K was a matrix differential operator with respect to variables transverse to x. Equation ( 6) has been already used by the some of us in several applied problems dealing with asymptotics near degeneracy points of different types: for Maxwell equations in the Earth-ionosphere waveguide [10] (with a non-invertible Γ), Maxwell equations in curvilinear coordinates near the smooth boundary of the convex body [11], the Timoshenko beam equations [12], and elastic wave equations [13]. It was also applied to investigation of liquid crystals [14].…”

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confidence: 99%

“…This is the method we apply in the present paper. The same method was used in our previous papers [10], [12], [13], [11] (although it was not always written explicitly), where different asymptotic situations for waveguide problems were considered.…”

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confidence: 99%

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Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Fialkovsky,

Perel

2019

Preprint

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An asymptotic approach for a Schroedinger type equation with a non selfadjoint slowly varying Hamiltonian of a special type is developed. The Hamiltonian is assumed to be the result of a small perturbation of an operator with a twofold degeneracy (turning) point, which can be diagonalized at this point. The non-adiabatic transformation of modes is studied in the case where two small parameters are dependent: the parameter characterizing an order of the perturbation is a square root of the adiabatic parameter. The perturbation of the Hamiltonian produces a close pair of simple degeneracy points. Two regimes of mode transformation for the Schroedinder type equation are identified: avoided crossing of eigenvalues, corresponding to complex degeneracy points, and an explicit unavoidable crossing (with real degeneracy points).Both cases are treated by a method of matched asymptotic expansions in the context of a unifying approach. An asymptotic expansion of the solution near a crossing point containing the parabolic cylinder functions is constructed, and the transition matrix connecting the coefficients of adiabatic modes to the left and to the right of the degeneracy point is derived.Results are illustrated by an example: fermion scattering governed by the Dirac equation.

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Section: B Main Resultsmentioning

confidence: 99%

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confidence: 99%

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Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Fialkovsky,

Perel

2019

Preprint

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“…This coordinate system has been applied recently in electromagnetic problems in [21,22]. Then we rewrite the Maxwell equation in matrix form by analogy with [23]. We consider an etalon cylindrical problem to find an anzats and an asymptotic parameter.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of surface plasmons on curved interface

Perel

Zaika

2011

Proceedings of the International Conference Days on Diffraction 2011

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Surface plasmon polaritons (SSP), moving along a smooth curved interface between two isotropic media with slowly varying dielectric permittivities and magnetic permeabilities and supporting SSP, are studied theoretically. Solutions of Maxwell equations are investigated within a small wavelength limit in the boundary layer of the wavelength order near the surface. An explicit asymptotic formula for an EM wave traveling along geodesics on the surface is obtained. An exponential factor reflects the distinction between the planar and curved cases. The curvature-dependent correction term in the exponent demonstrates a strong dependence on the transverse curvature and a weak dependence on the longitudinal curvature. The closer the parameters to the resonance case, the more pronounced this tendency. It is found that the attenuation of the SPP in the case of lossy media may be reduced by changing the curvature. If the signs of the magnetic permeability of the medium on both sides of the interface are opposite, the surface magnetic plasmon polariton may propagate. Its short-wavelength asymptotics is found.

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“…Landau and Zener (1932) pioneered solving the problem of non-adiabatic transitions near the point of intersection of molecular terrns, see [5]. Later interxtions of electromagnetic waves in magnetoionic plasma [GI, interaction of acoustic modes in liquid layers [7] tunneling of electrons in crystal [8], transformation of VLF waves in the Earthionosphere waveguides [9], and interaction of body [la] and surface E131 elastic waves in solid were described. Similar problems were approached also by researches having a piire mathematical motivations, e. g. [IO,111. We start with the time-harmonic case where we employ the technique similar to the one used in [9] in radio physics and borrowed in its essence Gom Quantum Mechanics [5].…”

Section: Introductionmentioning

confidence: 99%

An asymptotic theory of resonance interaction of shear and bending modes in a non-uniform Timoshenko beam

Perel

Fialkovsky²,

Kiaelev³

2000

International Seminar Day on Diffraction Millennium Workshop (IEEE Cat. No.00EX450)

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An asymptotic theory of resonance interaction of shearand bending modes in a non-uniform Timoshenko beam Maria V. Perel, Ignat 17. Fialkovsky Physics Faculty, St.Petersburg University, K.ussia, Aleksei P. Kiselev Institute of Mechanical Engineering, Vasilievsky Ostrov Bolshoy Prospect 61, S t.Petersburg 199178, RussiaPropagation of modes in a smoothly non-uniform Timoshenko beam is considered. We present an asymptotic theory of interaction of two modes which phase velocities intersect at a single point and are non-tangent there. Highfrequency regime in the lime-harmonic case and propagation of discontinuities are both considered.

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Overexcitation of modes in an anisotropic earth-ionosphere waveguide on transequatorial paths in the presence of two close degeneracy points

Cited by 10 publications

References 2 publications

Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

Asymptotics of surface plasmons on curved interface

An asymptotic theory of resonance interaction of shear and bending modes in a non-uniform Timoshenko beam

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