Local density approximation for a perturbative equation of state
arXiv:cond-mat/0507711 · doi:10.1103/PhysRevA.72.063620
Abstract
The knowledge of a series expansion of the equation of state provides a deep insight into the physical nature of a quantum system. Starting from a generic ``perturbative'' equation of state of a homogeneous ultracold gas we make predictions for the properties of the gas in the presence of harmonic confinement. The local density approximation is used to obtain the chemical potential, total and release energies, Thomas-Fermi size and density profile of a trapped system in three-, two-, and one- dimensional geometries. The frequencies of the lowest breathing modes are calculated using scaling and sum-rule approaches and could be used in an experiment as a high precision tool for obtaining the expansion terms of the equation of state. The derived formalism is applied to dilute Bose and Fermi gases in different dimensions and to integrable one-dimensional models. Physical meaning of expansion terms in a number of systems is discussed.
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References in corpus (5)
- Observation of Bose-Einstein Condensation of Molecules
- Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
- Weakly bound dimers of fermionic atoms
- Collective excitations of a degenerate gas at the BEC-BCS crossover
- Equation of state and collective frequencies of a trapped Fermi gas along the BEC-unitarity crossover
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