Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2008-11-17
New J. Phys 11 (2009) 023011 (pp1-19)
Physics
Condensed Matter
Other Condensed Matter
22 pages, 5 figures
Scientific paper
10.1088/1367-2630/11/2/023011
In the case of tight transverse confinement (cigar-shaped trap) the three-dimensional (3D) nonlinear Schr\"odinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length $|a|\to \infty$), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion number $N$ the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a two-dimensional form is also performed for a tight axial confinement (disk-shaped trap). The resultant effective 2D nonpolynomial equation also produces results in agreement with the original 3D equation and has simple power-law nonlinearity for small and large $N$. For both cigar- and disk-shaped superfluids our nonpolynomial Schr\"odinger equations are quite attractive for phenomenological application.
Adhikari Sadhan K.
Salasnich Luca
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