Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar measures
Guarneri I, Schulz-Baldes H (1999)
Publication Type: Journal article
Publication year: 1999
Journal
Publisher: World Scientific Publishing
Book Volume: 11
Pages Range: 1249-1268
URI: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=98-382
DOI: 10.1142/S0129055X99000398
Abstract
We study a class of one-sided Hamiltonian operators with spectral measures given by invariant and ergodic measures of dynamical systems of the interval. We analyse dimensional properties of the spectral measures and prove upper bounds for the asymptotic spread in time of wavepackets. These bounds involve the Hausdorff dimension of the spectral measure, multiplied by a correction calculated from the dynamical entropy, the density of states, and the capacity of the support. For Julia matrices, the correction disappears and the growth is ruled by the fractal dimension.
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APA:
Guarneri, I., & Schulz-Baldes, H. (1999). Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar measures. Reviews in Mathematical Physics, 11, 1249-1268. https://doi.org/10.1142/S0129055X99000398
MLA:
Guarneri, Italo, and Hermann Schulz-Baldes. "Upper bounds for quantum dynamics governed by Jacobi matrices with self-similar measures." Reviews in Mathematical Physics 11 (1999): 1249-1268.
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