Extension of Bogoliubov theory to quasi-condensates

Details Extension of Bogoliubov theory to quasi-condensates Extension of Bogoliubov theory to quasi-condensates

2002-12-20

arxiv.org/abs/cond-mat/0212523v2

Phys. Rev. A 67, 053615 (2003)

Physics

Condensed Matter

Statistical Mechanics

32 pages, 2 figures; typos corrected in revised version

Scientific paper

10.1103/PhysRevA.67.053615

We present an extension of the well-known Bogoliubov theory to treat low dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretisation in cells of size $l$. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two and three dimensions with no ultraviolet or infrared divergence. Furthermore this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, the first order and second order correlations functions of the field. Explicit calculations are done for homogeneous systems.

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