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{c}ois}, title = {Quantum {Dynamics} and generalized fractal dimensions: an introduction}, journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:18}, pages = {1--14}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2002-2003}, zbl = {02124144}, mrnumber = {2030713}, language = {en}, url = {http://archive.numdam.org/item/SEDP_2002-2003____A18_0/} }
TY - JOUR AU - Germinet, François TI - Quantum Dynamics and generalized fractal dimensions: an introduction JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:18 PY - 2002-2003 SP - 1 EP - 14 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_2002-2003____A18_0/ LA - en ID - SEDP_2002-2003____A18_0 ER -
%0 Journal Article %A Germinet, François %T Quantum Dynamics and generalized fractal dimensions: an introduction %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:18 %D 2002-2003 %P 1-14 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_2002-2003____A18_0/ %G en %F SEDP_2002-2003____A18_0
Germinet, François. Quantum Dynamics and generalized fractal dimensions: an introduction. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Talk no. 18, 14 p. http://archive.numdam.org/item/SEDP_2002-2003____A18_0/
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