Tuesday, October 9, 2012

1210.2006 (S. E. Gharashi et al.)

Three s-wave interacting fermions under anisotropic harmonic
confinement: Dimensional crossover of energetics and virial coefficients
   [PDF]

S. E. Gharashi, K. M. Daily, D. Blume
We present essentially exact solutions of the Schroedinger equation for three fermions in two different spin states with zero-range s-wave interactions under harmonic confinement. Our approach covers spherically symmetric, strictly two-dimensional, strictly one-dimensional, cigar-shaped, and pancake-shaped traps. In particular, we discuss the transition from quasi-one-dimensional to strictly one-dimensional and from quasi-two-dimensional to strictly two-dimensional geometries. We determine and interpret the eigenenergies of the system as a function of the trap geometry and the strength of the zero-range interactions. The eigenenergies are used to investigate the dependence of the second- and third-order virial coefficients, which play an important role in the virial expansion of the thermodynamic potential, on the geometry of the trap. We show that the second- and third-order virial coefficients for anisotropic confinement geometries are, for experimentally relevant temperatures, very well approximated by those for the spherically symmetric confinement for all s-wave scattering lengths.
View original: http://arxiv.org/abs/1210.2006

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