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, issue 1

Abstract: 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*. (ii) In the case γ > γ* , we also establish the following asymptotics for the number N(z) of eigenvalues of H below z 0), for all γ > γ*.

Date: 2013
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https://doi.org/10.1155/2013/875194

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:875194

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