On the spectrum of an Hamiltonian in Fock space. Discrete spectrum Asymptotics
Albeverio, Sergio ; Lakaev, Saidakhmat N. ; Rasulov, Tulkin H.
arXiv, 0508028 / Harvested from arXiv
Text on arXiv
A model operator $H$ associated with the energy operator of a system describing three particles in interaction, without conservation of the number of particles, is considered. The precise location and structure of the essential spectrum of $H$ is described. The existence of infinitely many eigenvalues below the bottom of the essential spectrum of $H$ is proved for the case where an associated generalized Friedrichs model has a resonance at the bottom of its essential spectrum. An asymptotics for the number $N(z)$ of eigenvalues below the bottom of the essential spectrum is also established. The finiteness of eigenvalues of $H$ below the bottom of the essential spectrum is proved if the associated generalized Friedrichs model has an eigenvalue with energy at the bottom of its essential spectrum.
Publié le : 2005-08-14
Classification:  Mathematical Physics,  Mathematics - Functional Analysis,  Primary: 81Q10, Secondary: 35P20, 47N50 
@article{0508028,
     author = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Rasulov, Tulkin H.},
     title = {On the spectrum of an Hamiltonian in Fock space. Discrete spectrum
  Asymptotics},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0508028}
}

Albeverio, Sergio; Lakaev, Saidakhmat N.; Rasulov, Tulkin H. On the spectrum of an Hamiltonian in Fock space. Discrete spectrum
  Asymptotics. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0508028/