An initial value representation for semiclassical time-correlation functions

Autor:	J. Liam McWhirter
Rok vydání:	2000
Předmět:	Density matrix Formalism (philosophy of mathematics) Matrix algebra Stationary phase Quantum mechanics General Physics and Astronomy Semiclassical physics Initial value problem Physical and Theoretical Chemistry Mathematics Time correlation Mathematical physics
Zdroj:	The Journal of Chemical Physics. 112:7891-7902
ISSN:	1089-7690 0021-9606
DOI:	10.1063/1.481392
Popis:	We derive a new initial value representation for semiclassical time-correlation functions. This derivation combines the initial value formalism developed by Miller with the stationary phase analysis of integrals over endpoint velocities developed by Xiao and Coker [J. Chem. Phys. 102, 496 (1995)] and more recently extended by Bonella, Ciccotti, and Coker [Molec. Phys. 62, 1203 (1996)]. As a result, the determination of the classical paths within the correlation function does not require “root” searches; furthermore, the thermal density matrix within this function weights the initial and not the final positions of these paths. To prevent the correlation function from being not a smooth function of time, a semiclassical phase index similar to the Maslov index is introduced. A simple numerical example is provided and possible criticisms of our approach are discussed.
Databáze:	OpenAIRE
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