Multiphonon excitations in boson quantum films

Dynamical excitations in thin liquid films of He-4 adsorbed to a substrate are investigated by using a microscopic theory of excitations that includes multiple-phonon scattering. We study the dispersion relation, excitation mechanisms, transition densities, and particle currents as a function of surface coverage. A primary new result is that we have included three-phonon scattering processes in the calculation of the dynamic structure function and the one-body current densities. With the exception that our ground state is determined by our variational theory, rather than taken from experiment, our work on the dynamic structure function is the generalization of that of Jackson [Phys. Rev. A 4, 2386 (1971)] to inhomogeneous systems (films). Using sum rules for the dynamic structure function as a guide, we suggest a simple scaling argument for improving the agreement between our dynamic structure function and the experimental one. The addition of three-phonon contributions bring about the following changes. First, the energy of most modes is lowered by a nonnegligible amount for finite momentum excitations. Second; the film's surface mode is the exception; it is only slightly affected. Third, for monolayer films there is large scattering at high energies at intermediate values of momenta. This scattering can be traced back to an,anomalously large contribution to the two-particle density of states. Fourth, all modes with energy above a critical energy decay, and the associated peaks of the dynamic structure function are broadened. Fifth, the maxonlike character is enhanced in the bulklike modes.