The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles

Abstract

A model operator associated with the energy operator of a system of three non conserved number of particles is considered. The essential spectrum of the operator is described by the spectrum of a family of the generalized Friedrichs model. It is shown that there are infinitely many eigenvalues lying below the bottom of the essential spectrum, if a generalized Friedrichs model has a zero energy resonance.

Key words: Operator energy, non conserved number of particles, eigenvalues, Efimov effect, Faddeev-Newton equations, essential spectrum, Hilbert-Schmidt operators, infinitely many eigenvalues.

Full Text

Article Information

Title	The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles
Source	Methods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 1-16
MathSciNet	MR2308575
Copyright	The Author(s) 2007 (CC BY-SA)

Authors Information

Sergio Albeverio
Institut fur Angewandte Mathematik, Universitat Bonn, Wegelerstr. 6, D-53115, Bonn, Germany; SFB 611, Bonn, Germany; BiBoS, Bielefeld, Germany; IZKS; CERFIM, Locarno, Switzerland; Accademia di Architettura, Mendrisio, Switzerland

Saidakhmat N. Lakaev
Samarkand State University, 15 University Boulevard, Samarkand, 703004, Uzbekistan

Tulkin H. Rasulov
Samarkand State University, 15 University Boulevard, Samarkand, 703004, Uzbekistan 

Citation Example

Sergio Albeverio, Saidakhmat N. Lakaev, and Tulkin H. Rasulov, The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles, Methods Funct. Anal. Topology 13 (2007), no. 1, 1-16.

BibTex

@article {MFAT368,
    AUTHOR = {Albeverio, Sergio and Lakaev, Saidakhmat N. and Rasulov, Tulkin H.},
     TITLE = {The Efimov effect for a model operator associated with the Hamiltonian of a non conserved number of particles},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {1-16},
      ISSN = {1029-3531},
  MRNUMBER = {MR2308575},
       URL = {http://mfat.imath.kiev.ua/article/?id=368},
}