Non-Hermitian scattering on a tight-binding lattice

Burke, Phillip C.; Wiersig, Jan; Haque, Masudul

doi:10.1103/PhysRevA.102.012212

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Non-Hermitian scattering on a tight-binding lattice

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Haque, Masudul
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Burke, P. C., Wiersig, J., & Haque, M. (2020). Non-Hermitian scattering on a tight-binding lattice. Physical Review A, 102(1): 012212. doi:10.1103/PhysRevA.102.012212.

Cite as: https://hdl.handle.net/21.11116/0000-0007-DD6B-9

Abstract

We analyze the scattering dynamics and spectrum of a quantum particle on a tight-binding lattice subject to a non-Hermitian (purely imaginary) local potential. The reflection, transmission, and absorption coefficients are studied as a function of the strength of this absorbing potential. The system is found to have an exceptional point at a certain strength of the potential. Unusually, all (or nearly all) of the spectrum pairs up into mutually coalescing eigenstate pairs at this exceptional point. At large potential strengths, the absorption coefficient decreases and the effect of the imaginary potential is similar to that of a real potential. We quantify this similarity by utilizing properties of a localized eigenstate.