2019/12/10 by Rafael Tiedra de Aldecoa, de Aldecoa, Rafael Tiedra
Computer Science · Physics and Astronomy · #46N50 #47A40 #81Q10 #81Q12 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum and electron transport phenomena #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.1912.04960
openalex publication_date 2019/12/10 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We present a general account on the stationary scattering theory for unitary\noperators in a two-Hilbert spaces setting. For unitary operators U0,U in\nHilbert spaces cal H0, cal H and for an identification operator\nJ: cal H0\→ cal H, we give the definitions and collect properties of\nthe stationary wave operators, the strong wave operators, the scattering\noperator and the scattering matrix for the triple (U,U0,J). In particular,\nwe exhibit conditions under which the stationary wave operators and the strong\nwave operators exist and coincide, and we derive representation formulas for\nthe stationary wave operators and the scattering matrix. As an application, we\nshow that these representation formulas are satisfied for a class of\nanisotropic quantum walks recently introduced in the literature.\n