Anyonic PT symmetry, drifting potentials and non-Hermitian delocalization

We consider wave dynamics for a Schrodinger equation with a non-Hermitian Hamiltonian H satisfying the generalized (anyonic) parity-time symmetry PTH = exp(2i phi)HPT, where P and T are the parity and time-reversal operators. For a stationary potential, the anyonic phase phi 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 phi not equal 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. Copyright (C) EPLA, 2019