6 papers
Semiclassical origin of the spectral gap for transfer operators of partially expanding map
Frédéric Faure
We consider a simple model of partially expanding map on the torus. We study the spectrum of the Ruelle transfer operator and show that in the limit of high frequencies in the neut…
Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances
Frederic Faure, Nicolas Roy, Johannes Sjoestrand
In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues…
Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula
Frederic Faure
We consider a nonlinear area preserving Anosov map M on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics…
Prequantum chaos: Resonances of the prequantum cat map
Frederic Faure
Prequantum dynamics has been introduced in the 70' by Kostant-Souriau-Kirillov as an intermediate between classical and quantum dynamics. In common with the classical dynamics, pre…
Ruelle-Pollicott resonances for real analytic hyperbolic map
Frederic Faure, Nicolas Roy
We study two simple real analytic uniformly hyperbolic dynamical systems: expanding maps on the circle S1 and hyperbolic maps on the torus T2. We show that the Ruelle-Pollicott res…
Loss of quantum coherence in a system coupled to a zero-temperature environment
A. Ratchov, F. Faure, F. W. J. Hekking
We discuss the influence of a zero-temperature environment on a coherent quantum system. First, we calculate the reduced density operator of the system in the framework of the well…