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 .
"On the Discrete Spectrum of a Model Operator in Fermionic Fock Space." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/875194