Stéphane Nonnenmacher

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(1.1) P (h) = −h∆+ V (x) , V ∈ C c (X) , X = R 2 , with hyperbolic classical flows, the smallness of dimension of the trapped set implies that there is a gap between the resonances and the real axis. In other words, the quantum decay rate is bounded from below if the classical repeller is sufficiently filamentary. The higher dimensional statement is given(More)
In this paper we construct a sequence of eigenfunctions of the “quantum Arnold’s cat map” that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a semiclassical limit measure that is the sum of 1/2 the normalized Lebesgue measure on the torus plus 1/2 the normalized Dirac(More)
1.1. Statement of the results. In this note we analyze simple models of classical chaotic open systems and of their quantizations. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller of the system. In a simplified(More)
These notes present a description of quantum chaotic eigenstates, that is bound states of quantum dynamical systems, whose classical limit is chaotic. The classical dynamical systems we will be dealing with are mostly of two types: geodesic flows on Euclidean domains (“billiards”) or compact riemannian manifolds, and canonical transformations on a compact(More)