  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.
