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Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, (4)He (bosons) and (3)He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon-roton mode in liquid (4)He by neutron scattering, verifying Landau's prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as 'zero-sound' in (3)He, and 'plasmons' in charged systems) and incoherent particle-hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau's theory of Fermi liquids. At higher wavevectors, the collective mode enters the particle-hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid (3)He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau's theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory.

Optimized variational calculations have been carried out for pure and doped clusters of He atoms up to a cluster size of N=1000 particles. For small cluster sizes with less than or equal to 112 particles, where comparisons with existing di8'usion Monte Carlo results are possible, we find excellent agreement for the ground-state energy, correlation, and structure functions. For larger clusters, our ground-state energies extrapolate smoothly toward a bulk limit of-7.2 K with a surface energy of 0.272 K A. The resulting ground-state densities show unmistakable oscillations, confirming our earlier conclusions based on difFusion Monte Carlo studies. The present study of large clusters allows us to bridge the gap between finite systems and the bulk limit. Specifically, we show how the bulk limit of collective energies is reached as well as how the bulk Feynman spectrum is reproduced in the 8-wave component of the dynamic structure function in large droplets. By plotting the collective excitation energy of higher multipole modes as a function of an effective wave number k = gE(E+ 1)/R, we show that the resulting spectrum can be directly compared with experimental excitation energies determined for plane liquid surfaces and films. By summing up to 8 = 50 partial wave components, we show that the full dynamic structure function simultaneously displays the phonon-roton and the ripplon excitation spectrum. In the case of helium droplets doped with impurities such as rare gas atoms or the SF6 molecule, we show that the dipole collective mode becomes unstable with increased droplet size, strongly indicating that these impurities are delocalized inside large droplets. The microscopic character of the instability is revealed in the excitation functions and transition densities of the dipole mode. The introduction of impurities also profoundly alters the dynamic structure function, severely "fragments" the Feynman spectrum, and obliterates landmark structures such as the maxon and the roton. ' ' ' ' are computationally quite straightforward. By construction, these theories rely on phenomenological inputs Rom systems other than the one under examination, and occasionally, as in the local density approximation, on systems that do not exist and cannot be produced in nature (uniform low density liquid helium). The validity of such an extrapolation into unphysical regimes must always be scrutinized. In particular, when two-dimensional substructures like layers or shells are part of the system under consideration, presently available phenomenological density functionals23, 3x have been proven to be unreliable. By use of our optimized variational theory, we have computed the ground-state energy, chemical potential, collective monopole, dipole, quadrupole, and higher multipole excitations, one and two-body densities, and the dynamic structure function for pure and doped (rare gas atoms and SFs) helium clusters up to size N = 1000.