Jinqiao Duan, Xin-Chu Fu, Pei-De Liu, Anthony Manning  Home/Search
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Abstract: We show that a linear quantum harmonic oscillator is chaotic in the sense of LiYorke. We also prove that the weighted backward shift map, used as an infinite dimensional linear chaos model, in a separable Hilbert space is chaotic in the sense of Li-Yorke, in addition to being chaotic in the sense of Devaney. Key words: infinite dimension, quantum oscillator, linear chaotic system 1 Introduction We consider an unforced quantum harmonic oscillator, i.e., a very small frictionless massspring... (Update)
Context of citations to this paper: More
.... shift operator) for a linear quantum harmonic oscillator is chaotic in the sense of Wiggins (or Devaney) Duan, Fu, Liu and Manning ([5]) have recently used result of the current paper to prove that this annihilation operator is also chaotic in the sense of Li Yorke. An...
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BibTeX entry: (Update)
J. Duan, X.-C. Fu, P.-D. Liu, and A. K. Manning, On a linear chaotic quantum harmonic oscillator, submitted, 1997. http://citeseer.ist.psu.edu/duan97linear.html More
@misc{ duan97linear,
author = "J. Duan and X. Fu and P. Liu and A. Manning",
title = "a linear chaotic quantum harmonic oscillator",
text = "J. Duan, X.-C. Fu, P.-D. Liu, and A. K. Manning, On a linear chaotic quantum
harmonic oscillator, submitted, 1997.",
year = "1997",
url = "citeseer.ist.psu.edu/duan97linear.html" }
Citations (may not include all citations):176 An Introduction to Chaotic Dynamical Systems (context) - Devaney - 1986
134 Introduction to Applied Nonlinear Dynamical Systems and Chao.. (context) - Wiggins - 1990
111 Chaos in Classical and Quantum Mechanics (context) - Gutzwiller - 1990
104 Functional Analysis (context) - Yosida - 1978
23 Period three implies chaos (context) - Li, Yorke - 1975
5 the definition of chaos (context) - Kirchgraber, Stoffer - 1989
5 Introductory Quantum Mechanics (context) - Liboff - 1992
3 invariant cyclic vector manifolds (context) - Godefroy, Shapiro et al. - 1991
2 Linear chaos in the unforced quantum harmonic oscillator (context) - Gulisashvili, MacCluer - 1996
2 Chaos and totally chaos (context) - Zhou - 1987
2 Infinite-dimensional linear dynamical systems with chaoticit.. - Fu, Duan - 1998
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