Abstract
We extend the Husimi (coherent state) based version of linearized semiclassical theories for the calculation of correlation functions to the case of survival probabilities. This is a case that could be dealt with before only by use of the Wigner version of linearized semiclassical theory. Numerical comparisons of the Husimi and the Wigner case with full quantum results as well as with full semiclassical ones will be given for the revival dynamics in a Morse oscillator with and without coupling to an additional harmonic degree of freedom.
Highlights
The quest for a simplified description of quantum dynamics of many body systems in terms of classical dynamical input has recently become ever more prominent [1]
linearized semiclassical initial value representation (LSC-IVR) are close in spirit to the diagonal approximation that is used to calculate the smooth part of the semiclassical spectral density in chaotic systems [14]
The first goal was to highlight that the Wigner-Weyl and Husimi transform version of linearized semiclassical theories can lead to the same final formula, whereas they are quite different in the case of the survival probability, where strictly, the simple Husimi version is not applicable
Summary
The quest for a simplified description of quantum dynamics of many body systems in terms of classical dynamical input has recently become ever more prominent [1]. The classical Wigner method in chemical physics is referred to as linearized semiclassical initial value representation (LSC-IVR) and is prominently used by the Miller group [8,9,10]. Whereas in the pioneering works of the Heller as well as the Miller groups, Wigner transforms in the LSC-IVR are used, a new semiclassical framework, introduced by Antipov, Ye and Ananth [15], based on Husimi functions, see [16,17], can be tuned to reproduce existing quantum-limit and classical-limit SC approximations to quantum real-time correlation functions. Two possible classical approximations will be discussed and because the Husimi version is less general than the Wigner form, in Section 3, a new approach to the survival probability will be laid out. Detailed analytical calculations of determinants of block matrices whose results are needed in the main text can be found in the Appendixes A and B
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