Resonance regimes of scattering by small bodies with impedance boundary conditions

Lakshtanov, Evgeny; Vainberg, Boris

doi:10.1088/1751-8113/43/41/415205

Cited by 7 publications

(6 citation statements)

References 20 publications

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“…For example, the boundary conditions with purely imaginary Λ = iΛ i for the 1D and 2D geometries are extensively used [90][91][92][93][94] in the actively developing field of PT -symmetric quantum mechanics [95][96][97]. Apart from the purely theoretical interest [98], the analysis of the systems with the complex Robin lengths has large practical applications as they model scattering phenomena in different media [99]. Consider, for example, electromagnetic or acoustical processes when the wave vector k from (1) is the ratio of the actual frequency ω and the speed c of the propagation of the corresponding oscillations: It is well known that a porous lining of the walls of the sound duct results in nonzero and, in general, complex acoustical admittance Y [100].…”

Section: Introductionmentioning

confidence: 99%

Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

Olendski¹

2011

Annals of Physics

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Solutions of the scalar Helmholtz wave equation are derived for the analysis of the transport and thermodynamic properties of the two-dimensional disk and three-dimensional infinitely long straight wire in the external uniform longitudinal magnetic field B under the assumption that the Robin boundary condition contains extrapolation length Λ with nonzero imaginary part Λ i . As a result of this complexity, the self-adjointness of the Hamiltonian is lost, its eigenvalues E become complex too and the discrete bound states of the disk characteristic for the real Λ turn into the corresponding quasibound states with their lifetime defined by the eigenenergies imaginary parts E i . Accordingly, the longitudinal flux undergoes an alteration as it flows along the wire with its attenuation/amplification being E i -dependent too. It is shown that, for zero magnetic field, the component E i as a function of the Robin imaginary part exhibits a pronounced sharp extremum with its magnitude being the largest for the zero real part Λ r of the extrapolation length. Increasing magnitude of Λ r quenches the E i − Λ i resonance and at very large Λ r the eigenenergies E approach the asymptotic real values independent of Λ i . The extremum is also wiped out by the magnetic field when, for the large B, the energies tend to the Landau levels. Mathematical and physical interpretations of the obtained results are provided; in particular, it is shown that the finite lifetime of the disk quasibound states stems from the Λ i -induced currents flowing through the sample boundary. Possible experimental tests of the calculated effect are discussed; namely, it is argued that it can be observed in superconductors by applying to them the external electric field E normal to the surface.

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Section: Introductionmentioning

confidence: 99%

Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

Olendski¹

2011

Annals of Physics

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“…Then from (22) it follows that u 0 ∞ is analytic in λ. The function u ∞ is also analytic in λ, ℑλ ≥ 0, (see eg [4], [5]). Thus, f λ (θ 0 ) is analytic when ℑλ ≥ 0, and the contour of integration in (55) can be replaced by the contour Γ = Γ 1 ∪ Γ 2 ∪ Γ 3 defined in Fig.…”

Section: Real Impedancementioning

confidence: 99%

High Frequency Scattering by a Classically Invisible Body

Lakshtanov¹,

Sleeman²,

Vainberg³

2012

SIAM J. Appl. Math.

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We consider a polyhedron with zero classical resistance, i.e., a polyhedron invisible to an observer viewing only the paths of geometrical optics rays. The corresponding problem of scattering of plane waves by the polyhedron is studied. The quasiclassical approximation is obtained and justified in the case of impedance boundary conditions with a non zero absorbing part. It is shown that the total momentum transmitted to the obstacle vanishes when the frequency k goes to infinity, and that the total cross section oscillates at high frequencies. When the impedance λ 0 is real (i. e., there is no absorption), it is shown that there exists a sequence of frequencies k n such that the averages in the impedance of the total cross section over shrinking intervals around λ 0 go to zero as k n → ∞.

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“…For example, it is immediately seen from Eqs. (68) that in the asymptotic cases the energy is real when the following conditions hold:…”

Section: Field-free Casementioning

confidence: 99%

“…If the extrapolation length Λ can take negative values, a natural question arises: what happens if the Robin parameter is complex? Attempts to answer it have been made during the study of the scattering phenomena in different media [68] such as a sound duct with porous lining [69][70][71][72][73][74][75][76], impedance electromagnetic waveguides [77], ferrite-filled resonator systems [78], absorbers in high-frequency electromagnetic scattering [79]. A comprehensive answer showed that for the infinitely long cylinder with singly connected circular cross section the imaginary part of the transverse complex energy E ⊥ exhibits a pronounced maximum as a function of the imaginary part Λ i of the de Gennes distance [1].…”

Section: Introductionmentioning

confidence: 99%

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

Olendski¹

2012

Annals of Physics

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Properties of the two-dimensional ring and three-dimensional infinitely long straight hollow waveguide with unit width and inner radius ρ0 in the superposition of the longitudinal uniform magnetic field B and Aharonov-Bohm flux are analyzed within the framework of the scalar Helmholtz equation under the assumption that the Robin boundary conditions at the inner and outer confining walls contain extrapolation lengths Λin and Λout, respectively, with nonzero imaginary parts. It is shown that, compared to the disk geometry, the annulus opens up additional possibilities of varying magnetization and currents by tuning imaginary components of the Robin parameters on each confining circumference; in particular, the possibility of restoring a lossless longitudinal flux by zeroing imaginary part Ei of the total transverse energy E is discussed. The energy E turns real under special correlation between the imaginary parts of Λin and Λout with the opposite signs what corresponds to the equal transverse fluxes through the inner and outer interfaces of the annulus. In the asymptotic case of the very large radius, simple expressions are derived and applied to the analysis of the dependence of the real energy E on Λin and Λout. New features also emerge in the magnetic field influence; for example, if, for the quantum disk, the imaginary energy Ei is quenched by the strong intensities B, then for the annulus this takes place only when the inner Robin distance Λin is real; otherwise, it almost quadratically depends on B with the corresponding enhancement of the reactive scattering. Closely related problem of the hole in the otherwise uniform medium is also addressed for real and complex extrapolation lengths with the emphasis on the comparative analysis with its dot counterpart.

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Resonance regimes of scattering by small bodies with impedance boundary conditions

Cited by 7 publications

References 20 publications

Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

Resonant alteration of propagation in guiding structures with complex Robin parameter and its magnetic-field-induced restoration

High Frequency Scattering by a Classically Invisible Body

Guiding structures with multiply connected cross sections: Evolution of propagation in external fields at complex Robin parameters

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