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Interacting Bose gas: mean field and fluctuations revisited
1Laboratoire de Physique, ENS Lyon and CNRS, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
We describe Bose gas thermodynamic properties using imaginary-time Green functions. This method simply shows Bose-Einstein condensation and provides corrections beyond mean-field theory.
Area of Science:
- Thermodynamics
- Quantum Statistics
- Condensed Matter Physics
Background:
- Understanding Bose gas thermodynamic properties is crucial for quantum statistics.
- Mean-field theory provides a basic approximation but lacks accuracy in certain regimes.
- Previous methods for analyzing Bose gas condensation can be complex.
Purpose of the Study:
- To present a novel description of Bose gas thermodynamic properties.
- To derive the presence of off-diagonal long-range order (Bose-Einstein condensation) simply.
- To determine asymptotic corrections to mean-field theory using Kac's scaling.
Main Methods:
- Utilizing the hierarchy of equations for imaginary-time Green functions.
- Applying Kac's scaling to a repulsive binary potential.
- Comparing results with rigorous solutions and the Hartree-Fock approximation.
Main Results:
- A simple derivation of Bose-Einstein condensation for an ideal Bose gas.
- The analysis remains simple at the mean-field theory level.
- Asymptotic corrections to mean-field theory were determined for states far from condensation.
Conclusions:
- The Green function hierarchy offers a straightforward approach to Bose gas properties.
- The derived corrections improve upon standard mean-field approximations.
- The Hartree-Fock approximation is shown to be incomplete for these systems.
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