Abstract
We consider a model operator ${\mathbf H}_{\mu\lambda},$ $\mu,\lambda \geq 0$ associated with the energy operator of a lattice system describing two identical bosons and one particle, another nature in interactions, without conservation of the number of particles. The existence of infinitely many negative eigenvalues of ${\mathbf H}_{0\lambda}$ is proved for the case where the associated Friedrichs model have a zero energy resonance and an asymptotics of the form ${\mathcal U}_0 |\log|z||$ for the number of eigenvalues of ${\mathbf H}_{0\lambda}$ lying below $z<0,$ is obtained. We find the conditions for the infiniteness of the number of eigenvalues located inside (in the gap, in the below of the bottom) of the essential spectrum of ${\mathbf H}_{\mu\lambda}$.
Citation
M. I. Muminov. T. H. Rasulov. "Embedded Eigenvalues of a Hamiltonian in Bosonic Fock Space." Commun. Math. Anal. 17 (1) 1 - 22, 2014.
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