ORBITAL-FREE DENSITY FUNCTIONALS FOR FERMION GASES

Abstract

One approach to the orbital-free density functional theory for fermion gases is the density-potential functional formalism, which circumvents the problem of approximating the kinetic energy density functional. Under this formalism, we focus on the particle density and relate it to the time-evolution operator, which is approximated using the Suzuki-Trotter approximation. This approximation systematically produces a hierarchy of increasingly accurate approximate densities, with the simplest recovering the Thomas-Fermi result. When applied to exactly solvable systems, these approximate densities agree well with the exact solution. This approach is applied to two-component Fermi gases in a harmonic trap with contact interactions, where a phase transition between isotropic and anisotropic densities is found. Applications to the same system with dipolar interactions are discussed, and its ability to calculate properties for systems with large particle numbers can potentially predict behaviors testable in experiment. In addition, the most accurate approximation of the time-evolution operator considered in this project has applications in classical and quantum dynamics evolutions.