量子波导中的时间延迟和短程散射
Time delay and short-range scattering in quantum waveguides
摘要：
虽然许多物理参数占使用修改后的定义的时间延迟在多通道型散射过程中，人们很难找到严格的结果在这个问题上的文献。我们试图填补这一空白显示，无论是在一个抽象的设置和在一个短距离的情况下，修改后的时间延迟和艾森巴德-维格纳时间延迟波导的身份。在短程情形下，我们也得到了极限吸收原理，总哈密顿量的态谱性质，证明了波算子的存在性，并给出了S-矩阵的显式表达式。证明依赖于固定和换向器的方法。
英文摘要：
Although many physical arguments account for using a modified definition of time delay in multichannel-type scattering processes, one can hardly find rigorous results on that issue in the literature. We try to fill in this gap by showing, both in an abstract setting and in a short-range case, the identity of the modified time delay and the Eisenbud-Wigner time delay in waveguides. In the short-range case we also obtain limiting absorption principles, state spectral properties of the total Hamiltonian, prove the existence of the wave operators and show an explicit formula for the S-matrix. The proofs rely on stationary and commutator methods.
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