Efficient Diagonalization of Kicked Quantum Systems

Details Efficient Diagonalization of Kicked Quantum Systems Efficient Diagonalization of Kicked Quantum Systems

1997-12-17

arxiv.org/abs/cond-mat/9712209v2

Physica D131, 247 (1999)

Physics

Condensed Matter

Text reorganized; part on the kicked Harper model extended. 13 pages RevTex, 1 figure

Scientific paper

10.1016/S0167-2789(98)00230-9

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.

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