Quantum Dynamics and generalized fractal dimensions: an introduction
Séminaire Équations aux dérivées partielles (Polytechnique) (2002-2003), Talk no. 18, 14 p.

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 Transport Integrals and by the so called 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.

@article{SEDP_2002-2003____A18_0,
     author = {Germinet, Fran\c cois},
     title = {Quantum Dynamics and generalized fractal dimensions: an introduction},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2002-2003},
     note = {talk:18},
     mrnumber = {2030713},
     zbl = {02124144},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2002-2003____A18_0}
}
Germinet, François. Quantum Dynamics and generalized fractal dimensions: an introduction. Séminaire Équations aux dérivées partielles (Polytechnique) (2002-2003), Talk no. 18, 14 p. http://www.numdam.org/item/SEDP_2002-2003____A18_0/

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