Abstract
Chaos in classical systems will be reviewed. A test function for the existence of topological chaos, the Melnikov function, is shown to determine the existence of homoclinic points which imply classical topological chaos. The Melnikov function is generalized to semiclassical quantum ensembles and it is shown that quantum ensembles suppress the appearance of topological chaos. A kinetic equation is shown to exist governing fully quantum chaos. The conditions for its existence are new necessary conditions in the presence of quantum mechanics when classical topological ideas fail.
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Schieve, W.C., Petrosky, T.Y. (1986). Chaos in Simple Quantum Systems. In: Harvey, J.D., Walls, D.F. (eds) Quantum Optics IV. Springer Proceedings in Physics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71407-8_15
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DOI: https://doi.org/10.1007/978-3-642-71407-8_15
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