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Nonlinear variation of diffusion exponents in quantum dynamics. (English. Abridged French version) Zbl 0963.81024

Summary: We prove the existence of a nonlinear variation of the diffusion exponents in quantum dynamics. More precisely, we derive new lower bounds for the moments of order \(p\) associated to the state \(\psi(t)= e^{-itH} \psi\), and averaged in time between 0 and \(T\). These lower bounds are expressed in terms of generalized fractal dimensions \(D(1/(1+p/d))\) of the measure \(\mu_\psi\) (where \(d\) is the space dimension). This improves notably previous results, obtained in terms of Hausdorff and packing dimension.

MSC:

81Q50 Quantum chaos
81P20 Stochastic mechanics (including stochastic electrodynamics)
47N50 Applications of operator theory in the physical sciences
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