| Issue |
EPL
Volume 125, Number 1, January 2019
|
|
|---|---|---|
| Article Number | 10006 | |
| Number of page(s) | 7 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/125/10006 | |
| 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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