SURVIVAL PROBABILITIES OF COMPLEX GAUSSIAN WAVEPACKETS IN CHAOTIC AND REGULAR SYSTEMS BY THE LANCZOS RECURSION METHOD

The survival probability P(t) = \<phi-0\phi(t)>\2 for an initial complex Gaussian wavepacket phi-0 is calculated here for the first time by the Lanczos recursion method combined with the QL algorithm without computing the eigenfunctions of the Hamiltonian. Consequently, for an N x N Hamiltonian matrix the correct dynamical behaviour of the system is obtained by carrying out nN2 numerical operations rather than N3, where n is the number of Lanczos recursions. We show that when phi-0 is located in the regular region of the classical phase space the ratio n/N is smaller than in the case when it is located in the chaotic regime. This ratio is reduced as the values of t become smaller.