On the Dynamical Meaning of Spectral Dimensions

Details On the Dynamical Meaning of Spectral Dimensions On the Dynamical Meaning of Spectral Dimensions

1998-04-09

arxiv.org/abs/math-ph/9804009v1

Physics

Mathematical Physics

19 pages, LaTex, to appear in Ann. Inst. H. Poincare'

Scientific paper

Time averaging over the trajectory of a wavepacket up to time T defines a statistical operator (density matrix). The corresponding (Von Neumann) entropy is proven to asymptotically increase with time like D.log T, with D the Hausdorff dimension of the Local Density of States, at least if the latter measure has good scaling properties. In more general cases, spectral upper and lower bounds for the increase of entropy are given, in terms of the Hausdorff and of the Fractal Dimension of the Local Density of States.

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