On the discrete spectrum of a model operator in fermionic Fock space
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 genera...
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| Format: | Article |
| Language: | English |
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Hindawi Publishing Corporation
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/30052/ http://psasir.upm.edu.my/id/eprint/30052/1/30052.pdf |
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| author | Muminov, Zahriddin Ismail, Fudziah Eshkuvatov, Zainidin K. Rasulov, Jamshid |
| author_facet | Muminov, Zahriddin Ismail, Fudziah Eshkuvatov, Zainidin K. Rasulov, Jamshid |
| author_sort | Muminov, Zahriddin |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | 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 . |
| first_indexed | 2025-11-15T09:04:48Z |
| format | Article |
| id | upm-30052 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:04:48Z |
| publishDate | 2013 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-300522017-10-20T04:11:20Z http://psasir.upm.edu.my/id/eprint/30052/ On the discrete spectrum of a model operator in fermionic Fock space Muminov, Zahriddin Ismail, Fudziah Eshkuvatov, Zainidin K. Rasulov, Jamshid 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 . Hindawi Publishing Corporation 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30052/1/30052.pdf 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 http://www.hindawi.com/journals/aaa/2013/875194/ 10.1155/2013/875194 |
| spellingShingle | Muminov, Zahriddin Ismail, Fudziah Eshkuvatov, Zainidin K. Rasulov, Jamshid On the discrete spectrum of a model operator in fermionic Fock space |
| title | On the discrete spectrum of a model operator in fermionic Fock space |
| title_full | On the discrete spectrum of a model operator in fermionic Fock space |
| title_fullStr | On the discrete spectrum of a model operator in fermionic Fock space |
| title_full_unstemmed | On the discrete spectrum of a model operator in fermionic Fock space |
| title_short | On the discrete spectrum of a model operator in fermionic Fock space |
| title_sort | on the discrete spectrum of a model operator in fermionic fock space |
| url | http://psasir.upm.edu.my/id/eprint/30052/ http://psasir.upm.edu.my/id/eprint/30052/ http://psasir.upm.edu.my/id/eprint/30052/ http://psasir.upm.edu.my/id/eprint/30052/1/30052.pdf |