The relation between path-integral centroid variables [introduced by Jang and Voth: J. Chem. Phys. 111  , 2357 (1999)] and the coherent-state representation of quantum dynamics is analyzed. It is first noted that the projection of the phase-space centroid constrained Boltzmann operator onto an energy eigenstate yields a real but non-positive centroid quasi-density distribution function, exhibiting properties analogous to those of the corresponding Wigner function. By following Jang and Voth formalism, state-projected centroid symbols are defined and their exact dynamics identified. It is then shown that these new centroid symbols, which are complex valued functions, map onto the coherent state representation of quantum dynamics for the case of the ground state of the harmonic oscillator. The exact dynamics associated to other states of the harmonic oscillator is also analyzed. It is further shown that the state-projected centroid dynamics presented here retain full dynamical information at the ground state, which is proven to be otherwise unattainable through standard centroid dynamics. The implications of these findings for the use of classical phase-space methods in quantum mechanics is discussed.

Relationship between path-integral centroid variables and the coherent-state representation of quantum dynamics

246th National Meeting (2013)

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