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

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

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

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

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

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

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

scholarly journals A forbidden set for embedded eigenvalues

1994 ◽  
Vol 121 (1) ◽  
pp. 77-77
Author(s):  
Rafael René del Río Castillo
Keyword(s):  
Embedded Eigenvalues ◽  
Forbidden Set
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