Stéphane Nonnenmacher

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In this article we prove that for a large class of operators, including Schrödinger operators, 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.(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(More)
The color–flavor transformation is applied to the U (N c) lattice gauge model, in which the gauge theory is induced by a heavy chiral scalar field sitting on lattice sites. The flavor degrees of freedom can encompass several 'generations' of the auxiliary field, and for each generation, remaining indices are associated with the elementary plaquettes(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)
We study individual eigenstates of quantized area-preserving maps on the 2-torus which are classically chaotic. In order to analyze their semiclassical behavior, we use the Bargmann–Husimi representations for quantum states, as well as their stellar parametrization, which encodes states through a minimal set of points in phase space (the constellation of(More)
We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms(More)
We present an overview of mathematical results and methods relevant for the spectral study of semiclassical Schrödinger (or wave) operators of scattering systems, in cases where the corresponding classical dynamics is chaotic; more precisely, we assume that in some energy range, the classical Hamiltonian flow admits a fractal set of trapped trajectories,(More)