Impurity dynamics in boson quantum films

Abstract

We calculate the binding energy and dynamic properties of $^{3}\mathrm{He}$ atoms in films of $^{4}\mathrm{He}$ absorbed to graphite and several alkali metal substrates. Without adjustable parameters, we obtain excellent agreement with the experimental binding energies for the ground state of the $^{3}\mathrm{He}$ impurity. We then introduce a time-dependent variational wave function to calculate dynamic properties of the impurity. The motion of the impurity atom parallel to the surface is characterized by an effective mass due to hydrodynamic backflow. We also obtain the spectrum of excitation energies and the lifetime of the excited states. When both lifetime and backflow effects are included, the energy of the first excited state of the impurity and the effective mass of the ground state, agree well with experimental data.