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The semiclassical origin of curvature effects in universal spectral statistics

We consider the energy averaged two-point correlator of spectral determinants and calculate contributions beyond the diagonal approximation using semiclassical methods. Evaluating the contributions originating from pseudo-orbit correlations in the same way as in [S. Heusler {\textit {et al.}}\ 2007 Phys. Rev. Lett. {\textbf{98}}, 044103] we find a discrepancy between the semiclassical and the random matrix theory result. A complementary analysis based on a field-theoretical approach shows that the additional terms occurring in semiclassics are cancelled in field theory by so-called curvature effects. We give the semiclassical interpretation of the curvature effects in terms of contributions from multiple transversals of periodic orbits around shorter periodic orbits and discuss the consistency of our results with previous approaches.