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

Authors

  • S. 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
  • S. N. Lakaev Samarkand State University, 15 University Boulevard, Samarkand, 703004, Uzbekistan
  • T. H. Rasulov Samarkand State University, 15 University Boulevard, Samarkand, 703004, Uzbekistan 

DOI:

Keywords:

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

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.

Downloads

Published

2007-03-25

Issue

Vol. 13 No. 1 (2007)

Section

Articles

How to Cite

Albeverio, S., et al. “The Efimov Effect for a Model Operator Associated With the Hamiltonian of a Non Conserved Number of Particles”. Methods of Functional Analysis and Topology, vol. 13, no. 1, Mar. 2007, pp. 1-16, https://zen.imath.kiev.ua/index.php/mfat/article/view/332.