UPPER BOUNDS FOR QUANTUM DYNAMICS GOVERNED BY JACOBI MATRICES WITH SELF-SIMILAR SPECTRA

DOI10.1142/S0129055X99000398zbMath0969.81018MaRDI QIDQ4519828

Italo Guarneri, Hermann Schulz-Baldes

Publication date: 4 December 2000

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

spectral measuresHausdorff dimensionfractal dimensiondynamical entropywavepacketsinvariant and ergodic measuresdimensional propertiesJulia matricesone-sided Hamiltonian operatorsupper bounds for asymptotic spread

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (6)

Unnamed Item ⋮ Upper bounds on wavepacket spreading for random Jacobi matrices ⋮ Eigenvalue spacings and dynamical upper bounds for discrete one-dimensional Schrödinger operators ⋮ ASYMPTOTIC TIME DECAY IN QUANTUM PHYSICS: A SELECTIVE REVIEW AND SOME NEW RESULTS ⋮ Fractal dimensions and the phenomenon of intermittency in quantum dynamics ⋮ Progress in the mathematical theory of quantum disordered systems

Cites Work

• Unnamed Item
• Fractal wavelet dimensions and localization
• Remarks on the relation between quantum dynamics and fractal spectra
• Rigorous mean-field model for coherent-potential approximation: Anderson model with free random variables.
• Invariant sets under iteration of rational functions
• Quantum dynamics and decompositions of singular continuous spectra
• Anomalous Transport: A Mathematical Framework
• What Determines the Spreading of a Wave Packet?
• The multifractal analysis of Gibbs measures: Motivation, mathematical foundation, and examples
• Singular continuous spectra and discrete wave packet dynamics

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