Some spectral properties of the generalized Friedrichs model

1989 ◽  
Vol 45 (6) ◽  
pp. 1540-1563 ◽  
Author(s):  
S. N. Lakaev
Keyword(s):  
Spectral Properties ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model

Spectral properties of the generalized Friedrichs model

2010 ◽  
Vol 163 (1) ◽  
pp. 414-428 ◽  
Author(s):  
E. R. Akchurin
Keyword(s):  
Spectral Properties ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model

scholarly journals SOME SPECTRAL PROPERTIES OF THE NON-SELF-ADJOINT FRIEDRICHS MODEL OPERATOR

2005 ◽  
Vol 105A (2) ◽  
pp. 25-46
Author(s):  
Alexander V. Kiselev
Keyword(s):  
Spectral Properties ◽  
Model Operator ◽  
Friedrichs Model

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

Puiseux series expansion for an eigenvalue of the generalized Friedrichs model with perturbation of rank 1

2013 ◽  
Vol 46 (20) ◽  
pp. 205304 ◽  
Author(s):  
Saidakhmat Lakaev ◽  
Maslina Darus ◽  
Shaxzod Kurbanov
Keyword(s):  
Series Expansion ◽  
Puiseux Series ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model

On the spectral properties of the matrix-valued Friedrichs model

1991 ◽  
pp. 1-38 ◽  
Author(s):  
Zh. Abdullaev ◽  
S. Lakaev
Keyword(s):  
Spectral Properties ◽  
The Matrix ◽  
Friedrichs Model

scholarly journals On the Discrete Spectrum of a Model Operator in Fermionic Fock Space

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Zahriddin Muminov ◽  
Fudziah Ismail ◽  
Zainidin Eshkuvatov ◽  
Jamshid Rasulov
Keyword(s):  
Bound States ◽  
Fock Space ◽  
Critical Value ◽  
Efimov Effect ◽  
Model Operator ◽  
The Third ◽  
Direct Sum ◽  
Friedrichs Model ◽  
Number Of Particles ◽  
Generalized Friedrichs Model

We consider a model operatorHassociated with a system describing three particles in interaction, without conservation of the number of particles. The operatorHacts in the direct sum of zero-, one-, and two-particle subspaces of thefermionic Fock space ℱa(L2(𝕋3))overL2(𝕋3). We admit a general form for the "kinetic" part of the HamiltonianH, which contains a parameterγto distinguish the two identical particles from the third one. (i) We find a critical valueγ*for the parameterγthat allows or forbids the Efimov effect (infinite number of bound states if the associated generalized Friedrichs model has a threshold resonance) and we prove that only forγ<γ*the Efimov effect is absent, while this effect exists for anyγ>γ*. (ii) In the caseγ>γ*, we also establish the following asymptotics for the numberN(z)of eigenvalues ofHbelowz<Emin=infσessH:limz→EminNz/logEmin-z=𝒰0γ  𝒰0γ>0, for allγ>γ*.

Structure of the resonances of the generalized friedrichs model

1984 ◽  
Vol 17 (4) ◽  
pp. 317-319 ◽  
Author(s):  
S. N. Lakaev
Keyword(s):  
Friedrichs Model ◽  
Generalized Friedrichs Model

scholarly journals Threshold Effects for the Generalized Friedrichs Model with the Perturbation of Rank One

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Saidakhmat Lakaev ◽  
Arsmah Ibrahim ◽  
Shaxzod Kurbanov
Keyword(s):  
Threshold Effects ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Rank One ◽  
Friedrichs Model ◽  
Unique Eigenvalue ◽  
Generalized Friedrichs Model

A familyHμ(p),μ>0,p∈𝕋2of the Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the two-dimensional latticeℤ2is considered. The existence or absence of the unique eigenvalue of the operatorHμ(p)lying below threshold depending on the values ofμ>0andp∈Uδ(0)⊂𝕋2is proved. The analyticity of corresponding eigenfunction is shown.

scholarly journals INVESTIGATION OF THE SPECTRUM OF A GENERALIZED FRIEDRICHS MODEL: NON-INTEGRAL LATTICE CASE

2019 ◽  
Vol 3 (1) ◽  
pp. 5-11
Author(s):  
Tulkin Tulkin ◽  
◽  
Shokhida Nematova
Keyword(s):  
Discrete Spectrum ◽  
Interaction Parameter ◽  
Fock Space ◽  
The Self ◽  
Integral Lattice ◽  
Friedrichs Model ◽  
Generalized Friedrichs Model

The article investigates the essential and discrete spectrum of the self-adjoint generalized Friedrichs model. This model corresponds to a system consisting of no more than two particles on a non-integral lattice, and operates in a truncated subspace of Fock space. The number and location of eigenvalues is determined according to the "interaction parameter". Anobvious form of the eigenvectors is found

Resonant branch cuts in a generalized Friedrichs model

1996 ◽  
Vol 58 (5) ◽  
pp. 441-451 ◽  
Author(s):  
G. E. Rudin ◽  
M. Gadella
Keyword(s):  
Friedrichs Model ◽  
Branch Cuts ◽  
Generalized Friedrichs Model
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