Phase-Space Density Functional Theory: A Quasiclassical Approach

In time-dependent density functional theory, one obtains all observables pertaining to an interacting electronic system from one that is non-interacting, in principle exactly. In practice approximations are needed for the exchange-correlation potential and also observable-functionals. Although presently used functionals have been successful for many applications, they perform poorly for several phenomena of interest eg. momentum distributions, electronic quantum control problems, and where there is strong memory-dependence. We propose and explore a possible solution to these problems by extending TDDFT to phase-space densities, and discuss dynamical quasiclassical and semiclassical approximations for the correlation functional in phase-space.