Interference and quantization in semiclassical response functions

Application of the Herman-Kluk semiclassical propagator to the calculation of spectroscopic response functions for anharmonic oscillators has demonstrated the quantitative accuracy of these approximate dynamics. In this approach, spectroscopic response functions are expressed as multiple phase-space...

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Bibliographic Details
Published in:The Journal of chemical physics 2008-03, Vol.128 (12), p.124106-124106-12
Main Authors: Gruenbaum, Scott M., Loring, Roger F.
Format: Article
Language:English
Subjects:
ANHARMONIC OSCILLATORS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
INTEGRALS
INTERFERENCE
PHASE SPACE
PROPAGATOR
QUANTIZATION
RESPONSE FUNCTIONS
SEMICLASSICAL APPROXIMATION
TRAJECTORIES
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Summary:Application of the Herman-Kluk semiclassical propagator to the calculation of spectroscopic response functions for anharmonic oscillators has demonstrated the quantitative accuracy of these approximate dynamics. In this approach, spectroscopic response functions are expressed as multiple phase-space integrals over pairs of classical trajectories and their associated stability matrices. Here we analyze the Herman-Kluk semiclassical approximation to a linear response function and determine the origin of the capacity of this method to reproduce quantum effects in a response function from classical dynamical information. Our analysis identifies those classical trajectories that contribute most significantly to the response function on different time scales. This finding motivates a procedure for computing the linear response function in which the interference between pairs of classical trajectories is treated approximately, resulting in an integral over a single average trajectory, as in a purely classical calculation.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.2841943