2003/07/31 by Matthew J. Davis, M. J. Davis, S. A. Morgan · 63 citations
Mathematics · Physics and Astronomy · #Bose gas #Bose–Einstein condensate #Canonical ensemble #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Condensation #Cutoff #Equations of motion #Lattice (music) #Mathematics #Microcanonical ensemble #Monte Carlo method #Perturbation (astronomy) #Physics #Quantum many-body systems #Quantum mechanics #Statistical mechanics #Statistical physics #Strong Light-Matter Interactions #Thermodynamic limit #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreva.68.053615
published in Physical Review A 68(5) (American Physical Society) · v1: 9 pages, 5 figures, revtex 4. v2: additional text in response to referee's comments, now 11 pages, to appear in Phys. Rev. A
arxiv created 2003/10/02 · openalex publication_date 2003/11/24 · arxiv updated 2010/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a uv cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behavior of the specific heat.