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Non-hermitian Hamiltonians exhibiting PT-symmetry have sparked an extensive research
effort in recent years due to their intriguing property of allowing for a pseudo-hermitian phase with an all real
eigenvalue-spectrum [1]. This PT-symmetric phase in general will be spontaneously broken with the variation of a (gain/loss) parameter giving way to a phase of broken PT-symmetry with a fully or partially complex spectrum. Theoretical work on PT-systems spans from quantum field theory to solid state physics. Most recently, however, with the first experimental realizations of such systems using optical wave guides [2] the center of interest shifted onto photonic systems. Here I will present our recent results [3] on the influence of disorder on PT-symmetry breaking in tight binding models that can be used to describe light propagation in optical wave guide arrays. We find that disorder and localized modes result in an exponentially narrow exact PT-phase. We show, however, how the robustness of the pseudo-hermitian phase can be restored in dimer lattices that posses a generalized local PT-symmetry. We study the dynamics in lattices of such horizontally coupled dimers and show that the beam power it is governed by three universal regimes insensitive to microscopic details. [1] C. M. Bender, Rep. Prog. Phys. 70, 947-1018 (2007). [2] A. Guoet al., Phys. Rev. Lett. 103, (2009); C.E. Rüter et al, Nat Phys (2010). [3] O. Bendix, R. Fleischmann, T. Kottos, and B. Shapiro, Phys. Rev. Lett. 103(3):030402 (2009); O. Bendix, R. Fleischmann, T. Kottos, und B. Shapiro, J. Phys. A: Math. Theor. 43, 265305 (2010); M.C. Zheng, D.N. Christodoulides, R. Fleischmann, and T. Kottos (2010) Phys. Rev. A 82(1):010103(R) |
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