Quantum Dynamics and generalized fractal dimensions: an introduction

François Germinet[1]

  • [1] UMR 8524 CNRS, UFR de Mathématiques, Université de Lille 1, F-59655 Villeneuve d’Ascq Cédex, France

Séminaire Équations aux dérivées partielles (2002-2003)

  • Volume: 2002-2003, page 1-14

Abstract

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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 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.

How to cite

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Germinet, François. "Quantum Dynamics and generalized fractal dimensions: an introduction." Séminaire Équations aux dérivées partielles 2002-2003 (2002-2003): 1-14. <http://eudml.org/doc/11060>.

@article{Germinet2002-2003,
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 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.},
affiliation = {UMR 8524 CNRS, UFR de Mathématiques, Université de Lille 1, F-59655 Villeneuve d’Ascq Cédex, France},
author = {Germinet, François},
journal = {Séminaire Équations aux dérivées partielles},
language = {eng},
pages = {1-14},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Quantum Dynamics and generalized fractal dimensions: an introduction},
url = {http://eudml.org/doc/11060},
volume = {2002-2003},
year = {2002-2003},
}

TY - JOUR
AU - Germinet, François
TI - Quantum Dynamics and generalized fractal dimensions: an introduction
JO - Séminaire Équations aux dérivées partielles
PY - 2002-2003
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2002-2003
SP - 1
EP - 14
AB - 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.
LA - eng
UR - http://eudml.org/doc/11060
ER -

References

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