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

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.02.005· OSTI ID:21579907

Olendski, O ^[1]

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1. King Abdullah Institute for Nanotechnology, King Saud University, P.O. Box 2454, Riyadh 11451 (Saudi Arabia)

Highlights: > Solutions of the wave equation are analyzed for the confined circular geometry with complex Robin boundary conditions. > Sharp extremum is found in the energy dependence on the imaginary part of the extrapolation length. > Nonzero real part of the Robin length or/and magnetic field wipe out the resonance. - Abstract: 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 {Lambda} with nonzero imaginary part {Lambda}{sub 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 {Lambda} turn into the corresponding quasibound states with their lifetime defined by the eigenenergies imaginary parts E{sub i}. Accordingly, the longitudinal flux undergoes an alteration as it flows along the wire with its attenuation/amplification being E{sub i}-dependent too. It is shown that, for zero magnetic field, the component E{sub 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 {Lambda}{sub r} of the extrapolation length. Increasing magnitude of {Lambda}{sub r} quenches the E{sub i} - {Lambda}{sub i} resonance and at very large {Lambda}{sub r} the eigenenergies E approach the asymptotic real values independent of {Lambda}{sub 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 {Lambda}{sub 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.

• OSTI ID: 21579907
• Journal Information: Annals of Physics (New York), Vol. 326, Issue 6; Other Information: DOI: 10.1016/j.aop.2011.02.005; PII: S0003-4916(11)00034-0; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
ATTENUATION
BOUNDARY CONDITIONS
EIGENVALUES
ELECTRIC FIELDS
ENERGY DEPENDENCE
EXTRAPOLATION LENGTH
GINZBURG-LANDAU THEORY
HAMILTONIANS
MAGNETIC FIELDS
SCATTERING
SUPERCONDUCTORS
SURFACES
THERMODYNAMIC PROPERTIES
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS
DIFFERENTIAL EQUATIONS
DIMENSIONS
EQUATIONS
LENGTH
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
QUANTUM OPERATORS