Competing PT potentials and the re-entrant PT-symmetric phase: a particle in a box

We investigate the effects of competition between two complex, PT-symmetric potentials on the PT-symmetric phase of a 'particle in a box'. These potentials, given by VZ(x) = iZsign(x) and Vξ(x) = iξ[δ(x − a) − δ(x + a)], represent long-range and localized gain/loss regions, respectively. We obtain the PT-symmetric phase in the (Z, ξ) plane, and find that for locations ±a near the edge of the box, surprisingly, the PT-symmetric phase is strengthened by additional losses to the loss region. Consequently, we predict that a broken PT-symmetry will be restored by increasing the strength ξ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust PT-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, PT-symmetric potentials show unique, unexpected properties. (fast track communication)