Quasiclassical and semiclassical wave-packet dynamics in periodic potentials

The capability of quasiclassical and semiclassical methods to describe quantum dynamics in a periodic potential is investigated. Due to the periodicity of the potential, such systems may exhibit prominent quantum interference effects and, therefore, provide a particular challenge to methods based on classical approximations. Adopting a simple model for an isomerization reaction, we study the dynamics for different initial preparations as well as different dynamical observables. The quasiclassical calculations are based on the classical Wigner method and the semiclassical approach utilizes the Herman–Kluk (coherent state) initial-value representation, generalized to properly take into account the boundary conditions of the wave functions in a periodic potential. The results of the study show that the quasiclassical method can only describe the quantum dynamics in situations where the system is confined to the potential well and for highly averaged observables but fails otherwise. The semiclassical method, on the other hand, provides an excellent description of the quantum dynamics as long as the initial state is energetically separated from the torsional barrier. The reasons why the quasiclassical and semiclassical methods perform well in some situations but fail for others are discussed in some detail. Furthermore, the relation between the performance of the quasiclassical and semiclassical methods and the eigenvalue structure of the participating eigenstates is analyzed.

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