Discrete PT-symmetric lattices: spectral properties and stability of solitons
Abstract
In this work, the spectral properties of discrete PT-symmetric lattices and ring-shaped lattices, as well as the linear stability of PT-symmetric solitons in the nonlinear regime, are analyzed. In this case, the PT-symmetric potential is given in the form of a Gaussian potential, whose real part is equal to zero and whose imaginary part takes positive and negative values at each point. The results show that a phase transition occurs in the system at the PT-symmetry breaking point, which is characterized by the transition of the energy spectrum from real to complex values. It was shown that in the nonlinear regime, solitons are linearly stable in the unbroken PT-symmetric phase and linearly unstable in the broken PT-symmetric phase.
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