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

Journal Article · Wed Jan 15 00:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4861931· OSTI ID:22251650

Intissar, Abdelkader ^[1]

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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)

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.

• OSTI ID: 22251650
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
EIGENVALUES
HILBERT SPACE
MATHEMATICAL OPERATORS