Stationary scattering theory for unitary operators with an application to quantum walks
Stationary scattering theory for unitary operators with an application to quantum walks
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DOI：
10.1016/j.jfa.2020.108704
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发表时间：
2019-12
影响因子：
1.7
通讯作者：
R. T. Aldecoa
中科院分区：
文献类型：
--
作者：
R. T. Aldecoa
We present a general account on the stationary scattering theory for unitary operators in a two-Hilbert spaces setting. For unitary operators U 0, U in Hilbert spaces H 0, H and an identification operator J: H 0→ H, we give the definitions and collect properties of the stationary wave operators, the strong wave operators, the scattering operator and the scattering matrix for the triple (U, U 0, J). In particular, we exhibit conditions under which the stationary wave operators and the strong wave operators exist and coincide, and we derive representation formulas for the stationary wave operators and the scattering matrix. As an application, we show that these representation formulas are satisfied for a class of anisotropic quantum walks recently introduced in the literature.
