Quantum statistical dynamics with trajectories

Publication Type:

Journal Article

Authors:

Ciccotti, G.; Coker, D.F.; Kapral, R.

Source:

Springer Series in Chemical Physics, Volume 83, p.275-293 (2007)

ISBN:

9783540344582

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-59249088358&doi=10.1007%2f978-3-540-34460-5-12&partnerID=40&md5=621d7f6a8400cc52a5c471f9238f5f56

Abstract:

In this chapter we review the key issues in the construction of a mixed quantum-classical statistical mechanics. Two approaches are outlined: First, the construction of a formally consistent quantum-classical scheme which entails modified dynamical equations, and a modified equilibrium distribution that is the stationary state of the quantum-classical dynamics. Second, an approach which starts from the exact quantum correlation functions and introduces approximations for both the dynamics and (possibly separately) the equilibrium distribution. The first scheme is internally consistent, but inconsistencies arise in the properties of the quantum-classical correlation functions including the fact that time translation invariance and the Kubo identity are only valid to O(ℏ). The second scheme does not address the consistency issues explicitly, but has to provide suitable criteria for approximations for both the dynamics and the equilibrium distribution. Two approaches to the practical implementation of this second scheme are presented (1) a mixed quantum-classical propagation, closely related to the first scheme and (2) a linearized path integral approach.

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