2003/09/05 by Stefan Heusler, Sebastian Müller, Petr Braun +1 · 1 citation
Mathematics · Physics and Astronomy · #Geometry and complex manifolds #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #nlin.CD
paper · pdf · doi:10.1088/0305-4470/37/3/l02
published as J. Phys. A: Math. Gen. 37, L31 (2004) · 4 pages, 1 figure
arxiv created 2003/09/05 · openalex publication_date 2004/01/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We consider the semiclassical limit of the spectral form factor K (τ) of fully chaotic dynamics. Starting from the Gutzwiller-type double sum over classical periodic orbits we set out to recover the universal behaviour predicted by random-matrix theory, both for dynamics with and without time reversal invariance. For times smaller than half the Heisenberg time T H ∝ ℏ − f +1 , we extend the previously known τ-expansion to include the cubic term. Beyond confirming the random-matrix behaviour of individual spectra, the virtue of that extension is that the 'diagrammatic rules' come in sight which determine the families of orbit pairs responsible for all orders of the τ-expansion.