Abstract
Aiming at simplicity of explicit equations and, at the same time, controllable accuracy of the theory, we present our results for all the thermodynamic quantities and correlation functions for a weakly interacting Bose gas at short-to-intermediate distances obtained within an improved version of Beliaev's diagrammatic technique. With a controllably small (but essentially finite) Bogoliubov's symmetry-breaking term, Beliaev's diagrammatic technique becomes regular in the infrared limit. Up to higher-order terms (for which we present parametric order-of-magnitude estimates), the partition function and entropy of the system formally correspond to those of a non-interacting bosonic (pseudo-)Hamiltonian with a temperature-dependent Bogoliubov-type dispersion relation. Away from the fluctuation region, this approach provides the most accurate—in fact, the best possible within the Bogoliubov-type pseudo-Hamiltonian framework—description of the system with controlled accuracy. It produces accurate answers for the off-diagonal correlation functions up to distances where the behavior of correlators is controlled by generic hydrodynamic relations and, thus, can be accurately extrapolated to arbitrarily large scales. In the fluctuation region, the non-perturbative contributions are given by universal (for all weakly interacting U(1) systems) constants and scaling functions, which can be obtained separately—by simulating classical U(1) models—and then used to extend the description of the weakly interacting Bose gas to the fluctuation region. The technique works in all spatial dimensions, and we explicitly checked the validity of this technique against first-principle Monte Carlo simulations for various thermodynamic properties and the single-particle density matrix.
Highlights
For nearly half a century the theory of the weakly interacting Bose gases (WIBG) remained in the realm of purely theoretical investigations [1, 2, 4, 3, 5, 6, 7] providing insight into the nature of superfluid states of matter but not directly relating to existing experimental systems
Since 1995 both the theory of WIBG and experiments have progressed with a close relationship between the two [12]
To the well-known corrections to the ground state energy [14] and condensate density [1], to have a theory which accounts for leading corrections to all thermodynamic properties at finite temperature, works in any dimension, and provides estimates for omitted higher order terms
Summary
Follow this and additional works at: https://scholarworks.umass.edu/physics_faculty_pubs Part of the Physics Commons. Capogrosso-Sansone, B; Giorgini, S; Pilati, S; Pollet, L.; Prokof 'ev, N; Svistunov, B; and Troyer, M, "The Beliaev technique for a weakly interacting Bose gas" (2010). Authors B Capogrosso-Sansone, S Giorgini, S Pilati, L. N Prokof 'ev, B Svistunov, and M Troyer. This article is available at ScholarWorks@UMass Amherst: https://scholarworks.umass.edu/physics_faculty_pubs/1131. B Capogrosso-Sansone, S Giorgini, S Pilati, L Pollet, N Prokof ’ev, B Svistunov and M Troyer
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