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.