We study pseudo PT symmetry for a tight binding lattice with a general form of the modulation. Using high-frequency Floquet method, we show that the critical non-Hermitian degree for the reality of the spectrum can be manipulated by varying the parameters of the modulation. We study the effect of periodical and quasi-periodical nature of the modulation on the pseudo PT symmetry.

http://arxiv.org/abs/1411.3459
Quantum Physics (quant-ph); Mathematical Physics (math-ph)

PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of disorder for small number of lattice sites. We obtain the Hofstadter Butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserves the total intensity.

http://arxiv.org/abs/1402.2749
Quantum Physics (quant-ph)