Quantum scattering in quasi-one-dimensional cylindrical confinement

Journal Article · Sat Oct 15 00:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.042711· OSTI ID:20718747

Kim, J I; Schmiedmayer, J ^[1]; Schmelcher, P ^[1]

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1. Physikalisches Institut, Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg (Germany)

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.

• OSTI ID: 20718747
• Journal Information: Physical Review. A, Vol. 72, Issue 4; Other Information: DOI: 10.1103/PhysRevA.72.042711; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BINDING ENERGY
COLLISIONS
CONFINEMENT
CYLINDRICAL CONFIGURATION
D WAVES
DATA TRANSMISSION
ENERGY LEVELS
GEOMETRY
GREEN FUNCTION
ONE-DIMENSIONAL CALCULATIONS
ORBITAL ANGULAR MOMENTUM
PHASE SHIFT
POTENTIALS
QUANTUM WIRES
RESONANCE
SCATTERING
THREE-DIMENSIONAL CALCULATIONS
TWO-BODY PROBLEM
WAVE FUNCTIONS