Resonant alteration of propagation in guiding structures with complex Robin parameter and its magneticfieldinduced restoration
Abstract
Solutions of the scalar Helmholtz wave equation are derived for the analysis of the transport and thermodynamic properties of the twodimensional disk and threedimensional 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 selfadjointness 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.
 Publication:

Annals of Physics
 Pub Date:
 June 2011
 DOI:
 10.1016/j.aop.2011.02.005
 arXiv:
 arXiv:1103.0064
 Bibcode:
 2011AnPhy.326.1479O
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics;
 Physics  Classical Physics
 EPrint:
 Annals of Physics, vol. 326, # 6, pp. 14791500 (2011)