Adiabatic Approximation, Semiclassical Scattering, and Unidirectional Invisibility
arXiv:1401.4315 · doi:10.1088/1751-8113/47/12/125301
Abstract
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the -matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that the application of the adiabatic approximation to H(t) corresponds to the semiclassical description of the original scattering problem. In particular, the geometric part of the phase of the evolving eigenvectors of H(t) gives the pre-exponential factor of the WKB wave functions. We use these observations to give an explicit semiclassical expression for the transfer matrix. This allows for a detailed study of the semiclassical unidirectional reflectionlessness and invisibility. We examine concrete realizations of the latter in the realm of optics.
15 pages, 1 figure, 1 table, expanded version to appear in J. Phys. A
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Cited by in corpus (11)
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- Transfer Matrix Formulation of Scattering Theory in Two and Three Dimensions
- Non-Hermitian dynamics of slowly-varying Hamiltonians
- Unidirectional Invisibility and PT-Symmetry with Graphene
- Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
- Transmission of low-energy scalar waves through a traversable wormhole
- Low-frequency scattering defined by the Helmholtz equation in one dimension
- Oscillating potential well in complex plane and the adiabatic theorem
- Dynamical formulation of low-energy scattering in one dimension
- Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians
- Composition of Transfer Matrices for Potentials with Overlapping Support