Many-body Bose systems and the hard-sphere model: dynamic properties from the weak to the strong interaction regime

We obtain ab-initio estimations of the dynamic structure factor, S(q,ω), of Bose gases at zero temperature. More precisely, we use the Genetic Inversion via Falsification of Theories (GIFT) algorithm to perform analytic continuations of imaginary time correlation functions computed via an exact Path Integral projector method. Using the hard-sphere potential to model the two-body interactions between the atoms, we compute S(q,ω) changing the gas parameter from the dilute regime (na³ = 10⁻⁴) up to the density corresponding to superfluid ⁴He at equilibrium (na³ = 0.2138). With increasing density, we observe the emergence of a broad multiphonon contribution accompanying the quasiparticle peak and a crossover of the dispersion of elementary excitations from a Bogoliubov-like spectrum to a phonon-maxon- roton curve. Apart from the low wave vector region, for na³ = 0.2138 the energy-momentum dispersion relation and the static density response function, χ(q), turns out to be in good agreement with the superfluid ⁴He experimental data at equilibrium density.