一维离散Stark哈密顿量与杂质共振散射
One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities
摘要：
利用延拓理论的方法构造了一个一维离散Stark哈密顿量，该哈密顿量具有连续电场。在不含杂质的情况下，证明了该模型是精确可解的，谱是简单的、连续的、充满实轴的，并明确地构造了本征函数、预解式和谱测度.对于这个（未扰动）系统的共振谱是空的。利用算子延拓理论的方法，建立了考虑单节点杂质的模型。进行了谱分析，得到了预解奇异性的色散方程。的共振谱示出包含无限离散的共振集。建立了所构造的哈密顿量与某个李-弗里德里希模型的一一对应关系。
英文摘要：
A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.
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