Remarks on the relation between quantum dynamics and fractal spectra
The large time behaviour of various solutions of Schrödinger equations is studied by means of certain local and global dimensions of the spectral measure. Their relation to Hausdorff and correlation dimensions are given. The correlation dimensions control the time-decay of correlation functions. Growth exponents for moments of position operators are considered in terms of information dimension. The stability of such exponents under rank one perturbations is discussed. For such perturbations the dynamics is invariant in weak sense.
growth exponents for moments of position operators
scientific article; zbMATH DE number 1115573
scientific article