Over the past five years, open systems with balanced gain and loss have been investigated for extraordinary properties that are not shared by their closed counterparts. Non-Hermitian, Parity-Time (PT ) symmetric Hamiltonians faithfully model such systems. Such a Hamiltonian typically consists of a reflection-symmetric, Hermitian, nearest-neighbor hopping profile and a PT-symmetric, non-Hermitian, gain and loss potential, and has a robust PT -symmetric phase. Here we investigate the robustness of this phase in the presence of long-range hopping disorder that is not PT-symmetric, but is periodic. We find that the PT-symmetric phase remains robust in the presence of such disorder, and characterize the configurations where that happens. Our results are found using a tight-binding model, and we validate our predictions through the beam-propagation method.
Andrew K. Harter, Franck Assogba Onanga, and Yogesh N. Joglekar, "PT symmetry breaking in the presence of random, periodic, long-range hopping," Proc. SPIE 9920, Active Photonic Materials VIII, 99201O (Presented at SPIE Nanoscience + Engineering: August 31, 2016; Published: 16 September 2016); https://doi.org/10.1117/12.2239527.
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