On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the Spectrum of an Hamiltonian in Fock Space. Discrete Spectrum Asymptotics

Authors:

Sergio Albeverio Saidakhmat N. Lakaev Tulkin H. Rasulov

Affiliation:

1.Institut für Angewandte Mathematik,Universit?t Bonn,Bonn,Germany;2.SFB 611,Bonn, BiBos,Bielefeld–Bonn,Germany;3.CERFIM,Locarno and Acc.Arch,USI,Switzerland;4.Samarkand University, University Boulevard 15,Samarkand,Uzbekistan;5.Samarkand Division of Academy of Sciences of Uzbekistan,Samarkand,Uzbekistan

Abstract:

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 location of the essential spectrum of H is described. The existence of infinitely many eigenvalues (resp. the finiteness of eigenvalues) below the bottom τ_ess(H) of the essential spectrum of H is proved for the case where the associated Friedrichs model has a threshold energy resonance (resp. a threshold eigenvalue). For the number N(z) of eigenvalues of H lying below z < τ_ess(H) the following asymptotics is found

$limlimits_{z to tau_{rm ess}(H)-0}frac{N(z)}{|log |z-tau_{rm ess}(H)||}={U}_0 (0<{U}_0 <infty).$

Subject Classification: Primary: 81Q10, Secondary: 35P20, 47N50.

Keywords:

model operator conservation of number of particles Efimov effect infinitely many eigenvalues Birman-Schwinger principle essential spectrum Hilbert-Schmidt operator Friedrichs model conditionally negative definite function

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏