title: Computing thermal Wigner densities with the phase integration method.
abstract: We discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions [M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys. 109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly non-classical effects such as correlation among the momenta and coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems.
authors.affiliation: Département de Chimie, Ecole Normale Supérieure-PSL Research University, 24, rue Lhomond, 75005 Paris, France; Sorbonne Universités, UPMC Univ Paris 06, PASTEUR, F-75005 Paris, France; and CNRS, UMR 8640 PASTEUR, F-75005 Paris, France.
authors.forename: J
authors.initials: J
authors.lastname: Beutier
authors.affiliation: Département de Chimie, Ecole Normale Supérieure-PSL Research University, 24, rue Lhomond, 75005 Paris, France; Sorbonne Universités, UPMC Univ Paris 06, PASTEUR, F-75005 Paris, France; and CNRS, UMR 8640 PASTEUR, F-75005 Paris, France.
authors.forename: D
authors.initials: D
authors.lastname: Borgis
authors.affiliation: Département de Chimie, Ecole Normale Supérieure-PSL Research University, 24, rue Lhomond, 75005 Paris, France; Sorbonne Universités, UPMC Univ Paris 06, PASTEUR, F-75005 Paris, France; and CNRS, UMR 8640 PASTEUR, F-75005 Paris, France.
authors.forename: R
authors.initials: R
authors.lastname: Vuilleumier
authors.affiliation: Dipartimento di Fisica, Università di Roma "La Sapienza" Piazzale A. Moro 5, 00185 Rome, Italy.
authors.forename: S
authors.initials: S
authors.lastname: Bonella