MULTIPHONON EXCITATIONS IN BOSON QUANTUM FILMS

Dynamical excitations in thin liquid films of He-4 adsorbed to a subst rate are investigated by using a microscopic theory of excitations tha t includes multiple-phonon scattering. We study the dispersion relatio n, excitation mechanisms, transition densities, and particle currents as a function of surface coverage. A primary new result is that we hav e included three-phonon scattering processes in the calculation of the dynamic structure function and the one-body current densities. With t he exception that our ground state is determined by our variational th eory, rather than taken from experiment, our work on the dynamic struc ture function is the generalization of that of Jackson [Phys. Rev. A 4 , 2386 (1971)] to inhomogeneous systems (films). Using sum rules for t he dynamic structure function as a guide, we suggest a simple scaling argument for improving the agreement between our dynamic structure fun ction and the experimental one. The addition of three-phonon contribut ions bring about the following changes. First, the energy of most mode s is lowered by a nonnegligible amount for finite momentum excitations . Second; the film's surface mode is the exception; it is only slightl y affected. Third, for monolayer films there is large scattering at hi gh energies at intermediate values of momenta. This scattering can be traced back to an,anomalously large contribution to the two-particle d ensity of states. Fourth, all modes with energy above a critical energ y decay, and the associated peaks of the dynamic structure function ar e broadened. Fifth, the maxonlike character is enhanced in the bulklik e modes.