PT-symmetry breaking and maximal chirality in a nonuniform PT symmetric ring

We study the properties of an N-site tight-binding ring with parity and time-reversal (PT) symmetric, Hermitian, site-dependent tunneling and a pair of non-Hermitian, PT-symmetric, loss and gain impurities + or -i gamma . The properties of such lattices with open boundary conditions have been intensely explored over the past 2 years. We numerically investigate the PT-symmetric phase in a ring with a position-dependent tunneling function t sub( alpha )(k ) = [k(N ? k) super( alpha 2) that, in an open lattice, leads to a strengthened PT-symmetric phase, and study the evolution of the PT-symmetric phase from the open chain to a ring. We show that, generally, periodic boundary conditions weaken the PT-symmetric phase, although for experimentally relevant lattice sizes N ~ 50, it remains easily accessible. We show that the chirality, quantified by the (magnitude of the) average transverse momentum of a wave packet, shows a maximum at the PT-symmetric threshold. Our results show that although the wavepacket intensity increases monotonically across the PT-breaking threshold, the average momentum decays monotonically on both sides of the threshold.