Marche au hasard d’une quasi-particule massive dans le gaz de phonons d’un superfluide à très basse température

We consider in dimension 3 a homogeneous superfluid at very low temperature T having two types of excitations, (i) gapless acoustic phonons with linear dispersion relation wave number, and (ii) gapped γ quasiparticles quadratic (massive) the vicinity its extrema. Recent works [Nicolis Penco (2018), Castin, Sinatra Kurkjian (2017, 2019)], extending historical study by Landau Khalatnikov on phonon–roton interaction liquid helium 4, have explicitly determined scattering amplitude thermal phonon quasiparticle rest to leading order temperature. generalize this calculation case arbitrary subsonic group velocity, rigorous construction S matrix between exact asymptotic states, taking into account unceasing phonon–phonon phonon–γ interaction, which dresses incoming emerging virtual phonons; sheds new light Feynman diagrams scattering. In whole domain parameter space (wave number k, strength, etc.) where is energetically stable respect emission wavevector, we can therefore characterize erratic motion it performs due collisions phonons, through (a) mean force F(k) (b) longitudinal transverse momentum diffusion coefficients D ⫽ (k) ⊥ coming play Fokker–Planck equation, then, long times when has thermalized, (c) spatial coefficient