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

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 $\mathbf{B}$ under the assumption that the Robin boundary condition contains extrapolation length $\Lambda$ with nonzero imaginary part ${\Lambda }_i$. 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 $E_i$. 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 ${\Lambda }_r$ of the extrapolation length. Increasing magnitude of ${\Lambda }_r$ quenches the $E_i-{\Lambda }_i$ resonance and at very large ${\Lambda }_r$ the eigenenergies $E$ approach the asymptotic real values independent of ${\Lambda }_i$. 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 ${\Lambda }_i$-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 $\mathcal{E}$ normal to the surface.

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• From a Particle in a Box to the Uncertainty Relation in a Quantum Dot and to Reflecting Walls for Relativistic Fermions
• Perfect transmission scattering as a PT-symmetric spectral problem
• Curvature-induced bound states in Robin waveguides and their asymptotical properties
• Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum-information measures
• Comparative analysis of information measures of the Dirichlet and Neumann two-dimensional quantum dots
• Quantum information measures of the one-dimensional Robin quantum well
• The Pauli equation with complex boundary conditions
• Quantum-information theory of magnetic field influence on circular dots with different boundary conditions
• Rényi and Tsallis entropies of the Dirichlet and Neumann one-dimensional quantum wells
• Guiding structures with multiply connected cross-sections: evolution of propagation in external fields at complex Robin parameters
• Evolution of electric-field-induced quasibound states and resonances in one-dimensional open quantum systems