Open Access
2013 On the Discrete Spectrum of a Model Operator in Fermionic Fock Space
Zahriddin Muminov, Fudziah Ismail, Zainidin Eshkuvatov, Jamshid Rasulov
Abstr. Appl. Anal. 2013: 1-12 (2013). DOI: 10.1155/2013/875194


We consider a model operator H associated with a system describing three particles in interaction, without conservation of the number of particles. The operator H acts in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space  a ( L 2 ( 𝕋 3 ) ) over L 2 ( 𝕋 3 ) . We admit a general form for the "kinetic" part of the Hamiltonian H , which contains a parameter γ to distinguish the two identical particles from the third one. (i) We find a critical value γ * for the parameter γ that 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 for γ < γ * the Efimov effect is absent, while this effect exists for any γ > γ * . (ii) In the case γ > γ * , we also establish the following asymptotics for the number N ( z ) of eigenvalues of H below z < E m i n = inf σ e s s H : l im z E min N z / log E m i n - z = 𝒰 0 γ 𝒰 0 γ > 0 , for all γ > γ * .


Download Citation

Zahriddin Muminov. Fudziah Ismail. Zainidin Eshkuvatov. Jamshid Rasulov. "On the Discrete Spectrum of a Model Operator in Fermionic Fock Space." Abstr. Appl. Anal. 2013 1 - 12, 2013.


Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 07095454
MathSciNet: MR3064392
Digital Object Identifier: 10.1155/2013/875194

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
Back to Top