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A linear chaotic quantum harmonic oscillator

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1999Publisher:Elsevier BVJournal:Applied Mathematics Letters, volume 12, pages 15-19 (issn: 0893-9659,

Authors: Pei-De Liu; Xin-Chu Fu; Xin-Chu Fu; Anthony Manning; Jinqiao Duan;

doi: 10.1016/s0893-9659(98)00119-0

A linear chaotic quantum harmonic oscillator

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Abstract

This very brief article examines the chaoticity in the sense of Li and Yorke of two linear operators on \(L^2(\mathbb R)\). The first, which is known to be topologically transitive, is shown to support a chaotic set in the sense of Li and Yorke. This (a little unclearly) shows Li-Yorke-chaoticity of a quantum oscillator. The second (related), parameter dependent operator, which is known to be Devaney-chaotic, is analogously argued to be Li-Yorke-chaotic for a range of parameter values and non-chaotic for the rest.

Related Organizations

Chinese Academy of Sciences
China (People's Republic of)
Wuhan University
China (People's Republic of)
University of Warwick
United Kingdom
Clemson University
United States

Keywords

Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics), quantum oscillator, Applied Mathematics, Linear chaotic system, chaos in linear operators, types of chaos, Quantum chaos, Infinite dimension, Quantum oscillator, Strange attractors, chaotic dynamics of systems with hyperbolic behavior

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