Exactness of the Semi-Classical Approximation for Diffusion on Non-Compact Coset Spaces?
A disordered conductor in which the mean free path for inelastic electron scattering exceeds its size is called mesoscopic. Using the Landauer-Büttiker scattering approach one can express transport quantities in terms of a transfer matrix T which belongs to a non-compact group (Sp(2N,R),SU(N,N), and SO*(4N) for the orthogonal, unitary, and the symplectic transfer matrix ensembles, respectively)1. The evolution of the probability distribution of T with the length of a quasi-one-dimensional wire can be described as diffusion on the coset spaces of these groups. It is known that the semi-classical approximation for the path integral which describes diffusion on compact group manifolds is exact. Is this also true for these non-compact coset spaces?