Semiclassical maps: A study of classically forbidden transitions, sub-h structure, and dynamical localization

摘要: Representing the dynamics of a continuous time molecular system by symplectic discrete map can much reduce computational time. The question then arises whether semiclassical methods be effectively applied to this reduced description: as in classical case, should prove more computationally efficient description dynamics. Here we study propagation standard map, or kicked rotor, based on Herman–Kluk propagator. This is very interesting playground test feasibility mapping approach, since it demonstrates wealth quantum and dynamical behavior: As kick strength increases, goes from being nearly integrable, through mixed phase space, chaotic. displays phenomena that occur generic systems, so also how well semiclassics describe such phenomena. In particular, discuss (i) classically forbidden transport: significance branches integrand complex plane must understood order for meaningful; (ii) sub-h structure: integrable regime, poor due presence islets area less than Planck’s constant space; (iii) localization: chaotic momentum diffuses, whereas localizes. Our results show localizes, confirm directly theory localization largely interference.