Path integral methods dynamical properties

A disadvantage of using Car-Parrinello path integral methods is that the molecular dynamics is used only to compute averaged properties, the simulation dynamics having no direct physical meaning. A recently developed, albeit approximate method for generating fully quantum mechanical dynamics is the ab initio centroid molecular dynamics method (Marx et al., 1999 Pavese et al., 1999). Tlie application of Car-Parrinello methods to... 

The question then arises if a convenient mixed quantum-classical description exists, which allows to treat as quantum objects only the (small number of) degrees of freedom whose dynamics cannot be described by classical equations of motion. Apart in the limit of adiabatic dynamics, the question is open and a coherent derivation of a consistent mixed quantum-classical dynamics is still lacking. All the methods proposed so far to derive a quantum-classical dynamics, such as the linearized path integral approach [2,6,7], the coupled Bohmian phase space variables dynamics [3,4,9] or the quantum-classical Li-ouville representation [11,17—19], are based on approximations and typically fail to satisfy some properties that are expected to hold for a consistent mechanics [5,19]. 

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