160 research outputs found
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
We generalize the definition of quantum Anosov properties and the related
Lyapunov exponents to the case of quantum systems driven by a classical flow,
i.e. skew-product systems. We show that the skew Anosov properties can be
interpreted as regular Anosov properties in an enlarged Hilbert space, in the
framework of a generalized Floquet theory. This extension allows us to describe
the hyperbolicity properties of almost-periodic quantum parametric oscillators
and we show that their upper Lyapunov exponents are positive and equal to the
Lyapunov exponent of the corresponding classical parametric oscillators. As
second example, we show that the configurational quantum cat system satisfies
quantum Anosov properties.Comment: 17 pages, no figur
An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems
We construct an approximate renormalization scheme for Hamiltonian systems
with two degrees of freedom. This scheme is a combination of
Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. It
makes the connection between the approximate renormalization procedure derived
by Escande and Doveil, and a systematic expansion of the transformation. In
particular, we show that the two main approximations, consisting in keeping
only the quadratic terms in the actions and the two main resonances, keep the
essential information on the threshold of the breakup of invariant tori.Comment: 6 pages, RevTe
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