scholarly journals Virtual states and the generalized completeness relation in the Friedrichs model

2016 ◽  
Vol 94 (7) ◽  
Author(s):  
Zhiguang Xiao ◽  
Zhi-Yong Zhou
Keyword(s):  
Completeness Relation ◽  
Friedrichs Model

scholarly journals Quantum Zeno and anti-Zeno effects in the Friedrichs model

2001 ◽  
Vol 63 (6) ◽  
Author(s):  
I. Antoniou ◽  
E. Karpov ◽  
G. Pronko ◽  
E. Yarevsky
Keyword(s):  
Friedrichs Model

scholarly journals Understanding X(3862), X(3872), and X(3930) spectrum in a Friedrichs-model-like scheme

2018 ◽  
Vol 182 ◽  
pp. 02129
Author(s):  
Zhiguang Xiao ◽  
Zhi-Yong Zhou
Keyword(s):  
Quark Model ◽  
Good Accuracy ◽  
Bound State ◽  
P Wave ◽  
Hadron Interaction ◽  
Friedrichs Model ◽  
Charmonium States

In this talk, we review the method we proposed to use the Friedrichs-like model combined with QPC model to include the hadron interaction corrections to the spectrum predicted by the quark model, in particular the Godfrey-Isgur model. This method is then used on the first excited P-wave charmonium states, and X(3862), X(3872), and X(3930) state could be simultaneously produced with a quite good accuracy. The X(3872) state is shown to be a bound state with a large DD* continuum component. At the same time, the hc(2P) state is perdicted at about 3902 MeV with a pole width of about 54 MeV.

scholarly journals The Detectable Subspace for the Friedrichs Model: Applications of Toeplitz Operators and the Riesz–Nevanlinna Factorisation Theorem

2020 ◽  
Vol 21 (10) ◽  
pp. 3141-3156
Author(s):  
S. Naboko ◽  
I. Wood
Keyword(s):  
Toeplitz Operator ◽  
Finite Rank ◽  
Toeplitz Operators ◽  
Model Operator ◽  
Hardy Classes ◽  
Finite Rank Perturbation ◽  
Boundary Measurements ◽  
Independent Variable ◽  
Friedrichs Model

Abstract We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent variable) can be detected from ‘measurements on the boundary’. The framework of boundary triples is used to introduce the generalised Titchmarsh–Weyl M-function and the detectable subspaces which are associated with the part of the operator which is ‘accessible from boundary measurements’. In this paper, we choose functions arising as parameters in the Friedrichs model in certain Hardy classes. This allows us to determine the detectable subspace by using the canonical Riesz–Nevanlinna factorisation of the symbol of a related Toeplitz operator.

scholarly journals Description of the structure of singular spectrum for Friedrichs model operator near singular point

2001 ◽  
Vol 28 (1) ◽  
pp. 25-40
Author(s):  
Serguei I. Iakovlev
Keyword(s):  
Analytic Function ◽  
Singular Point ◽  
Uniqueness Theorem ◽  
Analytic Functions ◽  
Point Spectrum ◽  
Positive Imaginary Part ◽  
Model Operator ◽  
Real Roots ◽  
Singular Spectrum ◽  
Friedrichs Model

The study of the point spectrum and the singular continuous one is reduced to investigating the structure of the real roots set of an analytic function with positive imaginary partM(λ). We prove a uniqueness theorem for such a class of analytic functions. Combining this theorem with a lemma on smoothness ofM(λ)near its real roots permits us to describe the density of the singular spectrum.

Embedded eigenvalues and resonances of a generalized Friedrichs model

1995 ◽  
Vol 103 (1) ◽  
pp. 390-397 ◽  
Author(s):  
Zh. I. Abullaev ◽  
I. A. Ikromov ◽  
S. N. Lakaev
Keyword(s):  
Embedded Eigenvalues ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model

scholarly journals GENERALIZED EIGENVECTORS FOR RESONANCES IN THE FRIEDRICHS MODEL AND THEIR ASSOCIATED GAMOV VECTORS

2006 ◽  
Vol 18 (01) ◽  
pp. 61-78 ◽  
Author(s):  
HELLMUT BAUMGÄRTEL
Keyword(s):  
Hardy Space ◽  
Half Plane ◽  
Lower Half Plane ◽  
Linear Forms ◽  
Generalized Eigenvalues ◽  
Dirac Type ◽  
Generalized Eigenvectors ◽  
Upper Half Plane ◽  
Friedrichs Model ◽  
Generalized Eigenvector

A Gelfand triplet for the Hamiltonian H of the Friedrichs model on ℝ with multiplicity space [Formula: see text], [Formula: see text], is constructed such that exactly the resonances (poles of the inverse of the Livšic-matrix) are (generalized) eigenvalues of H. The corresponding eigen(anti)linear forms are calculated explicitly. Using the wave matrices for the wave (Möller) operators the corresponding eigen(anti)linear forms on the Schwartz space [Formula: see text] for the unperturbed Hamiltonian H0 are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector λ → k/(ζ0 - λ)-1, ζ0 resonance, [Formula: see text], which is uniquely determined by restriction of [Formula: see text] to [Formula: see text], where [Formula: see text] denotes the Hardy space of the upper half-plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup for t ≥ 0 of the Toeplitz type on [Formula: see text]. That is: Exactly those pre-Gamov vectors λ → k/(ζ - λ)-1, ζ from the lower half-plane, [Formula: see text], have an extension to a generalized eigenvector of H if ζ is a resonance and if k is from that subspace of [Formula: see text] which is uniquely determined by its corresponding Dirac type antilinear form.

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