00-365 J. M. Combes and G. Mantica

Fractal Dimensions and Quantum Evolution Associated with Sparse Potential Jacobi Matrices (361K, latex with 5 postscript figures) Sep 18, 00

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. We study the quantum dynamics generated via Schr\"odinger equation by sparse-potential Jacobi matrices on $l_2({\bf Z}_+)$. Exact bounds for the upper and lower intermittency functions governing the asymptotic growth of moments are derived in terms of the fractal dimensions of the spectral measure. Numerical experiments suggest that these bounds are sharp in the case of very sparse barriers.

Files: 00-365.src( 00-365.keywords , jmi6.tex , d1jl2p1.ps , d1ju23p1.ps , d2jl2p1.ps , d3ju23p1.ps , manyb.ps )