Condensate fluctuations in the dilute Bose gas
arXiv:cond-mat/0212221 · doi:10.1103/PhysRevA.71.043605
Abstract
The fluctuations of a number of particles in the Bose-Einstein condensate are studied in the grand canonical ensemble with an effective single-mode Hamiltonian, which is derived from an assumption that the mode corresponding to the Bose-Einstein condensate does not asymptotically correlate with other modes. The fluctuations are evaluated in the dilute limit with a proposed simple method, which is beyond the mean-field approximation. The accuracy of the latter is estimated; it is shown that the mean-field scheme does not work for the single-mode Hamiltonian, while for the Hartree Hamiltonian it allows us to estimate the condensate fluctuations up to a numerical factor. As a hypothesis, a formula is proposed that relates the fluctuations in the canonical ensemble with that of the grand canonical one.
arXiv comment8 pages, no figures
References in corpus (23)
- Theory of Bose-Einstein condensation in trapped gases
- A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
- Condensate fluctuations of a trapped, ideal Bose gas
- Anomalous fluctuations of the condensate in interacting Bose gases
- Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble
- Quantum kinetic theory IV: Intensity and amplitude fluctuations of a Bose- Einstein condensate at finite temperature including trap loss
- Canonical Statistics of Trapped Ideal and Interacting Bose Gases
- Phase transition of a Bose gas in a harmonic potential
- Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation
- The saddle-point method for condensed Bose gases
- Condensate statistics in interacting Bose gases: exact results
- Anomalous condensate fluctuations in strongly interacting superfluids
- Thermodynamic identities and particle number fluctuations in weakly interacting Bose--Einstein condensates
- Probing the statistical properties of Bose-Einstein condensates with light
- Short-range particle correlations in dilute Bose gas
- The kinetic and interaction energies of a trapped Bose gas: Beyond the mean field
- On the Structure of the Bose-Einstein Condensate Ground State
- Condensate fluctuations in finite Bose-Einstein condensates at finite temperature
- Number Fluctuation in an interacting trapped gas in one and two dimensions
- Anomalous fluctuations of two-dimensional Bose-Einstein condensates
- Dilute Bose gas: short-range particle correlations and ultraviolet divergence
- The Dilute Bose Gas Revised
- Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate