LONG-TIME DYNAMICS VIA DIRECT SUMMATION OF INFINITE CONTINUED FRACTIONS

Mori theory leads to in(finite) continued fractions [I(F)CF's] which upon inverse Laplace transformation (ILT) give the dynamical correlations in Hamiltonian systems. We propose a direct summation method to evaluate these ICF's, e.g., 1/[z + DELTA-1(z + ... to infinity)], by replacing them with FCF's with poles L = 10-zeta 2 less-than-or-equal-to zeta less-than-or-equal-to 5, for DELTA(mu) = mu(phi), phi < 2. Long-time dynamics is obtained upon an ILT of the ICF for 0 less-than-or-equal-to t less-than-or-equal-to tau with tau = f(phi,zeta) 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.