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Chaos, integrability, entanglement and decoherence

Thomas H. Seligman

Centro Internacional de Ciencias, and
Centro de Ciencias Físicas, UNAM,
Cuernavaca, Mexico

We shall give an unexpected view of the relation of decoherence and entanglement to the integrability or chaoticity of the underlying classical systems.

This view stems from the fact, that we shall consider separately the dependence on the dynamics from the dependence of the initial state, and not limit ourselves to the usual coherent states, as initial conditions. This has two reasons: First we believe that the phenomenon can be better understood in this fashion and second in the context of quantum computing we are certainly more interested in the evolution of a random initial state, than in the one of a Gaussian packet. We shall use both random matrix methods and correlation function techniques, as presented in the lectures of Dr. Prosen, to illuminate the problem at hand. We shall give close attention to the question, when decoherence follows the trend of the corresponding autocorrelation function (including fidelity in echo situations), and when not. We shall also inquire, if other correlation functions become relevant in situations where the autocorrelation function does not explain the behaviour of decoherence or entanglement.

Gorin T and Seligman T H 2002 J. Opt (in press) (quant-ph/0112030)
Gorin T and Seligman T H (nlin.CD/0101018)
Prosen T and Znidaric M 2002 J.Phys. A 35 1455
Prosen T and Seligman T H (nlin.CD/0201038)
Prosen T, Seligman T H and Znidaric M (quant-ph/0204043)

next up previous
Next: Shudo Up: Abstracts Previous: Schumacher