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J.I. Kim, Jörg Schmiedmayer, P. Schmelcher:
"Quantum scattering in quasi-one-dimensional cylindrical confinement";
Physical Review A, 72 (2005), 042711-1 - 042711-15.

Finite-size effects not only alter the energy levels of small systems, but can also lead to additional effective interactions within these systems. Here the problem of low-energy quantum scattering by a spherically symmetric short-range potential in the presence of a general cylindrical confinement is investigated. A Green's function formalism is developed which accounts for the full three-dimensional (3D) nature of the scattering potential by incorporating all phase shifts and their couplings. This quasi-1D geometry gives rise to scattering resonances and weakly localized states, whose binding energies and wave functions can be systematically calculated. Possible applications include, e.g., impurity scattering in ballistic quasi-1D quantum wires in mesoscopic systems and in atomic matter-wave guides. In the particular case of parabolic confinement, the present formalism can also be applied to pair collision processes such as two-body interactions. Weakly bound pairs and quasimolecules induced by the confinement and having zero or higher orbital angular momentum can be predicted, such as p- and d-wave pairings.

TONKS-GIRARDEAU GAS; IMPENETRABLE BOSONS; NEUTRAL ATOMS; TRAPPED GASES; WAVE-GUIDES; TRANSMISSION; REFLECTION; OBSTACLE; OPTICS; WIRES

http://aleph.ub.tuwien.ac.at/F?base=tuw01&func=find-c&ccl_term=AC06588218