Derek D. Scott, Yogesh N. Joglekar
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 $\pm i\gamma$. The properties of such lattices with open boundary conditions have been intensely explored over the past two years. We numerically investigate the PT-symmetric phase in a ring with a position-dependent tunneling function $t_\alpha(k)=[k(N-k)]^{\alpha/2}$ 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 $N \sim 50$, 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.
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http://arxiv.org/abs/1207.1945
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