Variational Formulation of Quantum Dynamics in Wigner Phase-Space

We have very recently derived and implemented the Dirac-Frenkel variational principle (VP) in the so-called Wigner Phase Space (WPS). WPS provides a complete quantum statistical framework for studying both dynamics and structure of statistical mixtures without any reference to wave functions. In WPS, the central objects are distribution functions (DF) and it is their structure and dynamics that are interesting. The structure and dynamics of these DF's are obtained by studying the Wigner-Liouville equation in imaginary and real time, respectively. The VP provides a systematically improvable way to solve this equation. An important feature of the method is that it works with trajectories of quantum particles which are intuitively appealing. The VP can for instance be applied for obtaining thermal Flux DFs that serve as input for the Classical Wigner model.