2000/12/31 by M. Sallé, M. Salle, Jan Smit +3 · 47 citations
Physics and Astronomy · #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Density matrix #Equipartition theorem #Gaussian #Hartree #High-Energy Particle Collisions Research #Magnetic field #Physics #Quantum #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Superposition principle #Thermalisation #hep-lat #hep-ph
paper · pdf · doi:10.1103/physrevd.64.025016
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 64(2) (American Physical Society) · 30 pages revtex including figures. Added clarifications
arxiv created 2001/06/15 · openalex publication_date 2001/06/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For homogeneous initial conditions, Hartree (Gaussian) dynamical approximations are known to have problems with thermalization because of insufficient scattering. We attempt to improve on this by writing an arbitrary density matrix as a superposition of Gaussian pure states and applying the Hartree approximation to each member of such an ensemble. Particles can then scatter via their back reaction on the typically inhomogeneous mean fields. Starting from initial states that are far from equilibrium we numerically compute the time evolution of particle distribution functions and observe that they indeed display approximate thermalization on intermediate time scales by approaching a Bose-Einstein form. However, for very large times the distributions drift towards classical-like equipartition.