On the dynamical meaning of spectral dimensions

Italo Guarneri

Displaying similar documents to “On the dynamical meaning of spectral dimensions”

On the asymptotic properties of quantum dynamics in the presence of a fractal spectrum

Italo Guarneri, Giorgio Mantica (1994)

Annales de l'I.H.P. Physique théorique

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Anomalous quantum transport in presence of self-similar spectra

J.-M. Barbaroux, H. Schulz-Baldes (1999)

Annales de l'I.H.P. Physique théorique

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Quantum Dynamics and generalized fractal dimensions: an introduction

François Germinet (2002-2003)

Séminaire Équations aux dérivées partielles

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We review some recent results on quantum motion analysis, and in particular lower bounds for moments in quantum dynamics. The goal of the present exposition is to stress the role played by quantities we shall call and by the so called of the spectral measure in the analysis of quantum motion. We start with very simple derivations that illustrate how these quantities naturally enter the game. Then, gradually, we present successive improvements, up to most recent result.

Multifractal analysis of nearly circular Julia set and thermodynamical formalism

P. Collet, R. Dobbertin, P. Moussa (1992)

Annales de l'I.H.P. Physique théorique

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Quantum diffusion and generalized Rényi dimensions of spectral measures

Jean-Marie Barbaroux, François Germinet, Serguei Tcheremchantsev (2000)

Journées équations aux dérivées partielles

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We estimate the spreading of the solution of the Schrödinger equation asymptotically in time, in term of the fractal properties of the associated spectral measures. For this, we exhibit a lower bound for the moments of order $p$ at time $T$ for the state $ψ$ defined by $[\frac{1}{T} \int_{0}^{T} ∥ | X |^{p / 2} e^{- i t H} ψ ∥^{2} d t]$ . We show that this lower bound can be expressed in term of the generalized Rényi dimension of the spectral measure $μ_{ψ}$ associated to the hamiltonian $H$ and the state $ψ$ . We especially concentrate on continuous models. ...

Multi-multifractal decomposition of digraph recursive fractals.

Dominique Simpelaere (2001)

Revista Matemática Iberoamericana

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In many situations, both deterministic and probabilistic, one is interested in measure theory in local behaviours, for example in local dimensions, local entropies or local Lyapunov exponents. It has been relevant to study dynamical systems, since the study of multifractal can be further developed for a large class of measures invariant under some map, particularly when there exist strange attractors or repelers (hyperbolic case). Multifractal refers to a notion of size, which emphasizes...