We consider wave dynamics for a Schrodinger equation with a non-Hermitian Hamiltonian H satisfying the generalized (anyonic) parity-time symmetry PT H = exp(2i)HPT , where P and T are the parity and time-reversal operators. For a stationary potential, the anyonic phase just rotates the energy spectrum of H in a 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 ≠= 0. In particular, in the unbroken 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.

Anyonic PT symmetry, drifting potentials and non-Hermitian delocalization

Longhi S.;Pinotti E.
2019

Abstract

We consider wave dynamics for a Schrodinger equation with a non-Hermitian Hamiltonian H satisfying the generalized (anyonic) parity-time symmetry PT H = exp(2i)HPT , where P and T are the parity and time-reversal operators. For a stationary potential, the anyonic phase just rotates the energy spectrum of H in a 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 ≠= 0. In particular, in the unbroken 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1127105
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