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Open Quantum Systems Decoherence Quantum Simulation

Anyonic mathcal{PT} symmetry, drifting potentials and non-Hermitian delocalization

arXiv
Authors: S. Longhi, E. Pinotti

Year

2018

Paper ID

39431

Status

Preprint

Abstract Read

~2 min

Abstract Words

131

Citations

N/A

Abstract

We consider wave dynamics for a Schrödinger equation with a non-Hermitian Hamiltonian mathcal{H} satisfying the generalized (anyonic) parity-time symmetry mathcal{PT H}= exp\(2 i varphi\) mathcal{HPT}, where mathcal{P} and mathcal{T} are the parity and time-reversal operators. For a stationary potential, the anyonic phase varphi just rotates the energy spectrum of mathcal{H} in complex plane, however for a drifting potential the energy spectrum is deformed and the scattering and localization properties of the potential show intriguing behaviors arising from the breakdown of the Galilean invariance when varphi neq 0. In particular, in the unbroken mathcal{PT} phase the drift makes a scattering potential barrier reflectionless, whereas for a potential well the number of bound states decreases as the drift velocity increases because of a non-Hermitian delocalization transition.

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  • We consider wave dynamics for a Schrödinger equation with a non-Hermitian Hamiltonian mathcalH satisfying the generalized (anyonic) parity-time symmetry mathcalPT H= exp(2 i...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1812.09462 [2] arXiv https://arxiv.org/abs/1812.09462 [3] Publisher https://arxiv.org/abs/1812.09462

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