Identification of semiclassical chaos in two-dimensional PT-symmetric systems

Abstract

Identification of regular and chaotic motions of two-dimensional PT-symmetric complex systems was investigated. New definitions have been introduced to study properties of trajectories in complex phase space. Projections of these trajectories on complex x- and y-planes, Lyapunov exponents, and surfaces of section have been used for identifying regular and irregular (chaotic) motions in complex phase space. Quantum level spacing distributions of these systems have also been calculated for finding out the connection between regular and irregular states with standard distributions such as Poisson and Wigner distributions. It has been found that the PT-symmetric complex systems behave in the same way as the real systems. PACS No.: 05.45.Ac