Browsing by Subject "scattering matrix"

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Access status: Restricted ,
Badanie operatorów $0$-zaburzonych za pomocą schematu Laxa-Phillipsa w teorii rozproszenia
(Data obrony: 2014-03-14) Rzepka, Barbara
Wydział Matematyki Stosowanej
Access status: Restricted ,
O zastosowaniu metrycznych grafów kwantowych w matematyce i fizyce
(Data obrony: 2013-07-17) Dudek, Dorota
Wydział Matematyki Stosowanej
Access status: Open Access ,
On the imaginary part of coupling resonance points
(Wydawnictwa AGH, 2019) Azamov, Nurulla A.; Daniels, Tom
We prove for rank one perturbations that the imaginary part of a coupling resonance point is inversely proportional by a factor of $-2$ to the rate of change of the scattering phase, as a function of the coupling variable, evaluated at the real part of the resonance point. This equality is analogous to the Breit-Wigner formula from quantum scattering theory. For more general relatively trace class perturbations, we also give a formula for the spectral shift function in terms of coupling resonance points, non-real and real.
Access status: Open Access ,
On the S-matrix of Schrödinger operator with nonlocal δ-interaction
(Wydawnictwa AGH, 2021) Główczyk, Anna; Kużel, Sergiusz
Schrödinger operators with nonlocal $\delta$-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is established. Two formulas for the $S$-matrix are obtained. The first one deals with the Krein-Naimark resolvent formula and the Weyl-Titchmarsh function, whereas the second one is based on modified reflection and transmission coefficients. The $S$-matrix $S(z)$ is analytical in the lower half-plane $\mathbb{C}_{−}$ when the Schrödinger operator with nonlocal $\delta$-interaction is positive self-adjoint. Otherwise, $S(z)$ is a meromorphic matrix-valued function in $\mathbb{C}_{−}$ and its properties are closely related to the properties of the corresponding Schrödinger operator. Examples of $S$-matrices are given.