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On the discrete spectrum of a model operator in fermionic Fock space


Muminov, Zahriddin and Ismail, Fudziah and Eshkuvatov, Zainidin K. and Rasulov, Jamshid (2013) On the discrete spectrum of a model operator in fermionic Fock space. Abstract and Applied Analysis, 2013. art. no. 875194. pp. 1-12. ISSN 1085-3375; ESSN: 1687-0409


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 (3)) over L 2 (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 .

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Official URL or Download Paper: http://www.hindawi.com/journals/aaa/2013/875194/

Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
DOI Number: https://doi.org/10.1155/2013/875194
Publisher: Hindawi Publishing Corporation
Keywords: Hamiltonian; Spectrum; Operator; Spectral properties
Depositing User: Umikalthom Abdullah
Date Deposited: 20 Jun 2014 06:56
Last Modified: 20 Oct 2017 04:11
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/875194
URI: http://psasir.upm.edu.my/id/eprint/30052
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