Efficient Diagonalization of Kicked Quantum Systems
Condensed Matter
2009-10-30 v2 chao-dyn
Chaotic Dynamics
Abstract
We show that the time evolution operator of kicked quantum systems, although a full matrix of size NxN, can be diagonalized with the help of a new method based on a suitable combination of fast Fourier transform and Lanczos algorithm in just N^2 ln(N) operations. It allows the diagonalization of matrizes of sizes up to N\approx 10^6 going far beyond the possibilities of standard diagonalization techniques which need O(N^3) operations. We have applied this method to the kicked Harper model revealing its intricate spectral properties.
Cite
@article{arxiv.cond-mat/9712209,
title = {Efficient Diagonalization of Kicked Quantum Systems},
author = {R. Ketzmerick and K. Kruse and T. Geisel},
journal= {arXiv preprint arXiv:cond-mat/9712209},
year = {2009}
}
Comments
Text reorganized; part on the kicked Harper model extended. 13 pages RevTex, 1 figure