On the Discrete Spectrum of a Model Operator in Fermionic Fock Space

Zahriddin Muminov, Fudziah Ismail, Zainidin Eshkuvatov and Jamshid Rasulov

Abstract and Applied Analysis, 2013, vol. 2013, 1-12

Abstract:

We consider a model operator associated with a system describing three particles in interaction, without conservation of the number of particles. The operator acts in the direct sum of zero-, one-, and two-particle subspaces of the fermionic Fock space  over . We admit a general form for the "kinetic" part of the Hamiltonian , which contains a parameter to distinguish the two identical particles from the third one. (i) We find a critical value for the parameter 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 the Efimov effect is absent, while this effect exists for any . (ii) In the case , we also establish the following asymptotics for the number of eigenvalues of below , for all .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:875194

DOI: 10.1155/2013/875194

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