2009/03/29 by Daniel Waltner, Stefan Heusler, Juan Diego Urbina +1
Mathematics · Physics and Astronomy · #Consistency (knowledge bases) #Curvature #Diagonal #Field (mathematics) #Interpretation (philosophy) #Quantum chaos and dynamical systems #Random Matrices and Applications #Random matrix #Semiclassical physics #Spectral Theory in Mathematical Physics #nlin.CD
paper · pdf · doi:10.1088/1751-8113/42/29/292001
published as J. Phys. A: Math. Theor. 42 292001 (2009)
arxiv created 2009/03/29 · openalex publication_date 2009/07/06 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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. 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.