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

Representing the dynamics of a continuous time molecular system by a symplectic discrete time map can much reduce the computational time. The question then arises of whether semiclassical methods can be effectively applied to this reduced description: as in the classical case, the map should prove to be a much more computationally efficient description of the dynamics. Here we study the semiclassical propagation of the standard map, or kicked rotor, based on a Herman-Kluk propagator. This is a very interesting playground to test the feasibility of a semiclassical mapping approach, since it demonstrates a wealth of quantum and classical dynamical behavior: As the kick strength increases, the system goes from being very nearly integrable, through mixed phase space, to chaotic. The map displays phenomena that occur in generic molecular systems, so this study is also a test of how well semiclassics can describe such phenomena. In particular, we discuss (i) classically forbidden transport: the significance of branches of the semiclassical integrand in the complex phase plane must be understood in order for the semiclassics to be meaningful; (ii) sub-h structure: in the nearly integrable regime, the semiclassics can be poor due to the presence of islets of area less than Planck's constant in phase space; (iii) dynamical localization: in the chaotic regime, the classical momentum diffuses, whereas the quantum localizes. Our results show that semiclassics also localizes, and we can confirm directly the theory that dynamical localization is due largely to phase interference. (C) 2000 American Institute of Physics. [S0021-9606(00)31202-8].