On the Discrete Spectrum of a Model Operator in Fermionic Fock Space
Joint Authors
Rasulov, Jamshid
Eshkuvatov, Zainidin K.
Ismail, Fudzliah
Muminov, Zahriddin
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-05-28
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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 ℱa(L2(?3)) over L2(?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
American Psychological Association (APA)
Muminov, Zahriddin& Ismail, Fudzliah& Eshkuvatov, Zainidin K.& Rasulov, Jamshid. 2013. On the Discrete Spectrum of a Model Operator in Fermionic Fock Space. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-505361
Modern Language Association (MLA)
Muminov, Zahriddin…[et al.]. On the Discrete Spectrum of a Model Operator in Fermionic Fock Space. Abstract and Applied Analysis No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-505361
American Medical Association (AMA)
Muminov, Zahriddin& Ismail, Fudzliah& Eshkuvatov, Zainidin K.& Rasulov, Jamshid. On the Discrete Spectrum of a Model Operator in Fermionic Fock Space. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-505361
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-505361