SHIFTED-UPDATE ROTATION - SIMPLE INTEGRATION OF THE MANY-LEVEL SCHRODINGER-EQUATION TO LONG TIMES

Shifted-update direct propagation algorithms are used to calculate the survival probabilities and spectra of a matrix-sealing model for vibr ational energy redistribution with 70 000 active states and nine degre es of freedom. A stabilized first-order method, shifted-update rotatio n has a simple geometrical interpretation, yet requires no storage ove rhead. Of the higher-order methods, only a third-order method executes faster in many cases, at the cost of stability and memory overhead. W e compare shifted-update methods to others applicable to sparse system s.