Jean-Marie Barbaroux, Francois Germinet, Serguei Tcheremchantsev
Fractal dimensions and the Phenomenon of Intermittency in Quantum 
Dynamics
(657K, .ps)

ABSTRACT.  We exhibit an intermittency phenomenon in quantum dynamics. More 
precisely we derive new lower bounds for the moments of order {\it p} 
associated to the state $\psi(t)={\rm e}^{-itH}\psi$ and averaged in 
time between $0$ and {\it T}. These lower bounds are expressed in 
terms of generalized fractal dimensions $D^\pm_{\mu_\psi}(1/(1+p/d))$ of the 
measure $\mu_\psi$ (where {\it d} is the space dimension). This 
improves notably previous results, obtained in terms of Hausdorff and 
Packing dimension.