Efficient Diagonalization of Kicked Quantum Systems
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 N2 ln(N) operations. It allows the diagonalization of matrizes of sizes up to N≈ 106 going far beyond the possibilities of standard diagonalization techniques which need O(N3) operations. We have applied this method to the kicked Harper model revealing its intricate spectral properties.
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