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Low dimensional Bose gases

2002; American Physical Society; Volume: 66; Issue: 1 Linguagem: Inglês

10.1103/physreva.66.013615

1538-4446

U. Al Khawaja, Jens O. Andersen, N. P. Proukakis, H. T. C. Stoof,

Quantum, superfluid, helium dynamics

We present an improved many-body T-matrix theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. The resulting mean-field theory is valid in arbitrary dimensions and able to describe the low-temperature crossover between three-, two-, and one-dimensional Bose gases. When applied to a degenerate two-dimensional atomic hydrogen gas, we obtain a reduction of the three-body recombination rate, which compares favorably with experiment. Supplementing the mean-field theory with a renormalization-group approach to treat the critical fluctuations, we also incorporate into the theory the Kosterlitz-Thouless transition that occurs in a homogeneous Bose gas in two dimensions. In particular, we calculate the critical conditions for the Kosterlitz-Thouless phase transition as a function of the microscopic parameters of the theory. The proposed theory is further applied to a trapped one-dimensional Bose gas, where we find good agreement with exact numerical results obtained by solving a nonlinear Langevin field equation.