Discrete Spectrum of a Model Operator Related to Three-Particle Discrete Schrödinger Operators

2009/04/14 by Tulkin H. Rasulov, Rasulov, Tulkin H.
Mathematics · #35P20 #47N50 #81Q10 #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0904.2078

openalex publication_date 2009/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A model operator H_μ, μ>0 associated to a system of three particles on the three-dimensional lattice ℤ³ that interact via nonlocal pair potentials is considered. We study the case where the parameter function w has a special form with the non degenerate minimum at the n, n>1 points of the six-dimensional torus \mathbbT⁶. If the associated Friedrichs model has a zero energy resonance, then we prove that the operator H_μ has infinitely many negative eigenvalues accumulating at zero and we obtain an asymptotics for the number of eigenvalues of H_μ lying below z, z<0 as z→ -0.

Related

• On the essential and discrete spectrum of a model operator related to three-particle discrete Schrödinger operators
• On the number of eigenvalues of a model operator associated to a system of three-particles on lattices
• Discrete spectrum asymptotics for the three-particle Hamiltonians on lattices
• On the spectrum of an Hamiltonian in Fock space. Discrete spectrum Asymptotics
• Estimates on the number of eigenvalues of two-particle discrete Schrödinger operators