Efficient diagonalization of kicked quantum systems

We show that the time-evolution operator of kicked quantum systems, althoug h a full matrix of size N x N, can be diagonalized with the help of a new m ethod based on a suitable combination of fast Fourier transform and Lanczos algorithm in just O(N-2 ln N) operations. It allows the diagonalization of matrices of sizes up to N approximate to 10(6) going far beyond the possib ilities of standard diagonalization techniques which need O(N-3) operations . We have applied this method to the kicked Harper model revealing its intr icate spectral properties. (C) 1999 Elsevier Science B.V All rights reserve d.