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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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Main Authors: Muminov, Zahriddin, Ismail, Fudziah, Eshkuvatov, Zainidin K., Rasulov, Jamshid
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30052/1/30052.pdf
http://psasir.upm.edu.my/id/eprint/30052/
http://www.hindawi.com/journals/aaa/2013/875194/
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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 .
format Article
author Muminov, Zahriddin
Ismail, Fudziah
Eshkuvatov, Zainidin K.
Rasulov, Jamshid
spellingShingle Muminov, Zahriddin
Ismail, Fudziah
Eshkuvatov, Zainidin K.
Rasulov, Jamshid
On the discrete spectrum of a model operator in fermionic Fock space
author_facet Muminov, Zahriddin
Ismail, Fudziah
Eshkuvatov, Zainidin K.
Rasulov, Jamshid
author_sort Muminov, Zahriddin
title 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_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_sort on the discrete spectrum of a model operator in fermionic fock space
publisher Hindawi Publishing Corporation
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30052/1/30052.pdf
http://psasir.upm.edu.my/id/eprint/30052/
http://www.hindawi.com/journals/aaa/2013/875194/
_version_ 1643829942688940032
score 13.211869

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