Barbaroux, Jean-Marie; Germinet, François; Tcheremchantsev, Serguei Nonlinear variation of diffusion exponents in quantum dynamics. (English. Abridged French version) Zbl 0963.81024 C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 5, 409-414 (2000). 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. Cited in 3 Documents MSC: 81Q50 Quantum chaos 81P20 Stochastic mechanics (including stochastic electrodynamics) 47N50 Applications of operator theory in the physical sciences Keywords:generalized fractal dimensions PDFBibTeX XMLCite \textit{J.-M. Barbaroux} et al., C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 5, 409--414 (2000; Zbl 0963.81024) Full Text: DOI