Fast time-evolution method for dynamical systems

A fast time-evolution method is developed for systems for which the dynamic al behavior can be reduced to the eigenvector/eigenvalue problem. The metho d does not use the eigenvectors/eigenvalues themselves and is based on a po lynominal expansion of the formal operator solution in the eigenfrequency d omain. It is complementary to the standard time-integration approaches and allows one to calculate or simulate the state of a system at arbitrary time s. The time evolution of, e.g., classical harmonic atomic systems and quant um systems described by linear Hamiltonians can be treated by this method.