Dynamics of liquid ${}^4\mathrm{He}$ in confined geometries from time-dependent density functional calculations

We present numerical results obtained from time-dependent density functional calculations of the dynamics of $\mathrm{liquid}{}^4\mathrm{He}$ in different environments characterized by geometrical confinement. The time-dependent density profile and velocity field of ${}^4\mathrm{He}$ are obtained by means of direct numerical integration of the nonlinear Schrödinger equation associated with a phenomenological energy functional which describes accurately both the static and dynamic properties of bulk liquid ${}^4\mathrm{He}.$ Our implementation allows for a general solution in three dimensions (i.e., no symmetries are assumed in order to simplify the calculations). We apply our method to study the real-time dynamics of pure and alkali-doped clusters, of a monolayer film on a weakly attractive surface and a nanodroplet spreading on a solid surface.