June 2012
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## Competing PT potentials and re-entrant PT symmetric phase for a particle in a box

Yogesh N. Joglekar, Bijan Bagchi

We investigate the effects of competition between two complex, $$\mathcal{PT}$$-symmetric potentials on the $$\mathcal{PT}$$-symmetric phase of a “particle in a box”. These potentials, given by $$V_Z(x)=iZ\mathrm{sign}(x)$$ and $$V_\xi(x)=i\xi[\delta(x-a)-\delta(x+a)]$$, represent long-range and localized gain/loss regions respectively. We obtain the $$\mathcal{PT}$$-symmetric phase in the $$(Z,\xi)$$ plane, and find that for locations $$\pm a$$ near the edge of the box, the $$\mathcal{PT}$$-symmetric phase is strengthened by additional losses to the loss region. We also predict that a broken $$\mathcal{PT}$$-symmetry will be restored by increasing the strength $$\xi$$ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust $$\mathcal{PT}$$-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, $$\mathcal{PT}$$-symmetric potentials show unique, unexpected properties.

http://arxiv.org/abs/1206.3310
Quantum Physics (quant-ph)