Long-time dynamics via direct summation of infinite continued fractions

Mori theory leads to in(finite) continued fractions [I(F)CFs] which upon inverse Laplace transformation (ILT) give the dynamical correlations in Hamiltonian systems. We propose a direct summation method to evaluate these ICFs, e.g., 1/[z+1/(z+...)], by replacing them with FCFs with poles L=102. Long-time dynamics is obtained upon an ILT of the ICF for 0 with being large. Our studies on dynamical correlations for boundary spins in S=1/2 XY chains agree very well with a recent exact solution for these correlations.