835 Identification of semiclassical chaos in two-dimensional PT -symmetric systems Asiri Nanayakkara and Chula Abayaratne 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 Résumé : Nous étudions l’identification des mouvements régulier et chaotique de systèmes en 2-D complexes à symétrie PT. Nous introduisons de nouvelles définitions pour étudier les propriétés des trajectoires dans un espace de phase complexe. Nous utilisons les projections sur les plans complexes x et y, les exposants de Lyapunov et les sections de surface pour identifier les mouvements réguliers et irréguliers (chaotiques) dans des espaces de phase complexes. Nous calculons aussi les distributions d’espacement des niveaux quantiques afin de déterminer la connexion entre les états réguliers et irréguliers et les distributions telles celles de Poisson et de Wigner. Nous trouvons ici que les systèmes à symétrie PT complexes ont un comportement très similaire aux systèmes réels. [Traduit par la Rédaction] 1. Introduction For a long time, it has been recognized that classical dynamics permits what is essentially ergodic behavior in systems with just a few degrees of freedom. The most well-known example of such systems is the Henon–Heiles Hamiltonian [1] that has been shown to undergo a transition from regular (quasi- periodic) classical trajectories to irregular (ergodic, chaotic) trajectories. For a real potential, regular trajectories occupy a limited amount of the energetically allowed phase space and have well-defined Poincaré surfaces of section. In this case, there exists a constant of motion in addition to energy. On the other hand, irregular trajectories appear to fill up the allowed phase space and have effectively random Poincaré surfaces [2] because of the absence of this additional constant of motion. To identify Received 6 June 2002. Accepted 15 December 2002. Published on the NRC Research Press Web site at http://cjp.nrc.ca/ on 29 July 2003. A. Nanayakkara. 1 Institute of Fundamental Studies, Hanthana Road, Kandy, Sri Lanka. C. Abayaratne. Department of Physics, University of Sri Jayawardenapura, Nugegoda, Sri Lanka. 1 Corresponding author (e-mail: asiri@ifs.ac.lk). Can. J. Phys. 81: 835–846 (2003) doi: 10.1139/P03-052 © 2003 NRC Canada