Linear Chaos in the Unforced Quantum Harmonic Oscillator

Author:

Gulisashvili A.1,MacCluer C. R.2

Affiliation:

1. Institute of Mathematics of the Georgian Academy of Sciences, Tbilisi, GA 380093

2. Department of Mathematics, Michigan State University, East Lansing, MI 48824

Abstract

The annihilation operator of the unforced quantum harmonic oscillator is chaotic.

Publisher

ASME International

Subject

Computer Science Applications,Mechanical Engineering,Instrumentation,Information Systems,Control and Systems Engineering

Reference15 articles.

1. Moon, F., Chaotic Vibrations, Wiley, New York, 1988.

2. Guckenheimer, J., and Holmes, P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, 2nd edition, New York, 1986.

3. Wiggins, S., Global Bifurcations and Chaos, Applied Mathematical Sciences, Vol. 73, Springer-Verlag, New York, 1988.

4. Godefroy G. , and ShapiroJ. H., “Operators with Dense, Invariant, Cyclic Vector Manifolds,” J. Functional Analysis, Vol. 98, p. 229229, 1991.

5. MacCluer C. R. , “Chaos in Linear Distributed Systems,” ASME JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL, Vol. 114, 1992, pp. 322–324.

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