准一维圆柱禁闭中的量子散射
Quantum Scattering in Quasi-1D Cylindrical Confinement
摘要：
有限尺寸效应不仅改变了小系统的能级，而且还可能导致这些系统内新的有效相互作用。本文研究了一般圆柱约束下球对称短程势的低能量子散射问题。一个格林函数形式主义的发展，占全3D性质的散射潜力，将所有的相移和它们的耦合。这种准一维几何结构产生散射共振和弱局域态，其结合能和波函数可以系统地计算。可能的应用包括例如在介观系统中的弹道准一维量子线和原子物质波波导中的杂质散射。在抛物约束的特殊情况下，本形式主义也可以应用到对碰撞过程，如两体相互作用。弱束缚对和准分子诱导的限制和具有零或更高的轨道角动量可以预测，如p-和d-波配对。
英文摘要：
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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