- 99-398 Jean-Marie Barbaroux, Francois Germinet, Serguei Tcheremchantsev
- Fractal dimensions and the Phenomenon of Intermittency in Quantum
Dynamics
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Oct 19, 99
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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.
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