Volume 125, Number 1, January 2019
|Number of page(s)||7|
|Published online||30 January 2019|
Anyonic symmetry, drifting potentials and non-Hermitian delocalization
1 Dipartimento di Fisica, Politecnico di Milano - Piazza L. da Vinci 32, I-20133 Milano, Italy
2 Istituto di Fotonica e Nanotecnlogie del Consiglio Nazionale delle Ricerche, sezione di Milano Piazza L. da Vinci 32, I-20133 Milano, Italy
Received: 31 July 2018
Accepted: 26 December 2018
We consider wave dynamics for a Schrödinger equation with a non-Hermitian Hamiltonian satisfying the generalized (anyonic) parity-time symmetry , where and are the parity and time-reversal operators. For a stationary potential, the anyonic phase φ just rotates the energy spectrum of 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 . In particular, in the unbroken 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.
PACS: 03.65.-w – Quantum mechanics / 11.30.Er – Charge conjugation, parity, time reversal, and other discrete symmetries / 03.65.Nk – Scattering theory
© EPLA, 2019
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