The topology of the off-diagonal terms of the semiclassical form factor

Abstract

The semiclassical origin of the logarithmic singularity at the Heisenberg time of the symplectic form factor is deduced by combining the result of M. Sieber and K. Richter for the first term of the loop-expansion in the orthogonal case with the contribution that arises due to the spin. We are able to make a quantitative statement about the topology of all non-diagonal contributions in terms of integrals over SU(2) leading to the conclusion that the same perturbative loop expansion is responsible for the form factor in the region $0 < \tau < 2$ in the orthogonal and symplectic case taking into account Kramers' degeneracy; the only difference being a phase factor arising due to the spin.