03-288 F. Germinet

Quantum Dynamics and generalized fractal dimensions: an introduction (479K, .ps) Jun 18, 03

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Abstract. 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 \emph{Transport Integrals} and by the so called \emph{generalized dimensions} 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.

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