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 ℱa(L2(𝕋3)) over L2(𝕋3). We admit a general...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/875194 |
| Summary: | 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(𝕋3)) over L2(𝕋3). 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<Emin=infσessH:limz→EminNz/logEmin-z=𝒰0γ 𝒰0γ>0, for all γ>γ*. |
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| ISSN: | 1085-3375 1687-0409 |