Comparison of the Quantum Mechanical Cumulant Expansion and the Semi-classical Curvature Expansion for Classically Chaotic Scattering Systems

Using the two-dimensional 3-disk system (in the A 1 representation) we compare the quantum mechanical cumulant expansion of the characteristic determinant, detM(k), and the semi-classical curvature expansion of the corresponding Gutzwiller-Voros zeta-function, Z GV (k). We will show that { independent of the wave number regime { the Gutzwiller-Voros curvature expansion is only an asymptotic approximation to the underlying exact quantum mechanical cumulant expansion and therefore only makes sense as a truncated series. This holds independently of whether the Gutzwiller-Voros curvature series itself converges or not, as the series deviates from the exact (absolutely converging) cumulant series already at nite curvature order, whereas the convergence property is determined by the innnite tail of the Gutzwiller-Voros series. The question whether the Gutzwiller-Voros expansion converges or not is therefore irrelevant with respect to the description of quantum mechanics.