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Title: A short note on the chaoticity of a weight shift on concrete orthonormal basis associated to some Fock-Bargmann space

Let F{sub α}(C) be the Hilbert space generated by the orthonormal basis e{sub n}{sup α,ν}(z)=((2ν)/(π) ){sup 1/4}e{sup (ν)/2} {sup z{sup 2}}e{sup −(π{sup 2)/(ν)}} {sup (n+α){sup 2+2iπ(n+α)z}};n∈N where ν > 0 and α are real numbers, this space is a particular case of (Γ, χ)-theta Fock-Bargmann spaces recently constructed by Ghanmi-Intissar [J. Math. Phys. 54, 063514 (2013)]. In the present work, we consider on F{sub α}(C) the weight shift operator M defined by Me{sub n}{sup α,ν}=ω{sub n}e{sub n+1}{sup α,ν},n∈N where ω{sub n}=c{sub α,ν}e{sup (2π)/(ν)n} and c{sub α,ν}=e{sup (π)/(ν)+2α} and we show the chaoticity of the operator H{sub p}=M{sup p}D{sup p+1};p=0,1,2,... where D is adjoint of M.
Authors:
 [1]
  1. Equiped’Analyse Spectrale, UMR-CNRS n: 6134, Université de Corse, Quartier Grossetti, 20 250 Corté, France and Le Prador, 129 rue du Commandant Rolland, 13008 Marseille (France)
Publication Date:
OSTI Identifier:
22251650
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; EIGENVALUES; HILBERT SPACE; MATHEMATICAL OPERATORS