dorsal/arxiv
View SchemaQuantum Scattering in Quasi-1D Cylindrical Confinement
| Authors | J. I. Kim, J. Schmiedmayer, P. Schmelcher |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506192 |
| URL | https://arxiv.org/abs/quant-ph/0506192 |
| DOI | 10.1103/PhysRevA.72.042711 |
Abstract
Finite size effects alter not only the energy levels of small systems, but can also lead to new 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 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 wavefunctions 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 quasi-molecules induced by the confinement and having zero or higher orbital angular momentum can be predicted, such as p- and d-wave pairings.
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"abstract": "Finite size effects alter not only the energy levels of small systems, but\ncan also lead to new effective interactions within these systems. Here the\nproblem of low energy quantum scattering by a spherically symmetric short range\npotential in the presence of a general cylindrical confinement is investigated.\nA Green\u0027s function formalism is developed which accounts for the full 3D nature\nof the scattering potential by incorporating all phase-shifts and their\ncouplings. This quasi-1D geometry gives rise to scattering resonances and\nweakly localized states, whose binding energies and wavefunctions can be\nsystematically calculated. Possible applications include e.g. impurity\nscattering in ballistic quasi-1D quantum wires in mesoscopic systems and in\natomic matter wave guides. In the particular case of parabolic confinement, the\npresent formalism can also be applied to pair collision processes such as\ntwo-body interactions. Weakly bound pairs and quasi-molecules induced by the\nconfinement and having zero or higher orbital angular momentum can be\npredicted, such as p- and d-wave pairings.",
"arxiv_id": "quant-ph/0506192",
"authors": [
"J. I. Kim",
"J. Schmiedmayer",
"P. Schmelcher"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall"
],
"doi": "10.1103/PhysRevA.72.042711",
"title": "Quantum Scattering in Quasi-1D Cylindrical Confinement",
"url": "https://arxiv.org/abs/quant-ph/0506192"
},
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