2000/03/31 by Martin Sieber · 1 citation
Mathematics · Physics and Astronomy · #Chaotic #Chaotic systems #Diagonal #Limit (mathematics) #Parametric statistics #Perturbation (astronomy) #Point (geometry) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Spectral density #Spectral properties #nlin.CD
paper · pdf · doi:10.1088/0305-4470/33/36/301
published as J. Phys. A 33 (2000) 6263 · LaTeX, 21 pages, 7 figures, small corrections, new references added
arxiv created 2000/08/14 · openalex publication_date 2000/09/01 · arxiv updated 2010/03/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K (τ) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown for order τ 2 and τ 3 that off-diagonal contributions to the form factor which involve diffractive orbits cancel exactly the diagonal contributions from diffractive orbits, implying that the perturbation by the scatterer does not change the spectral statistic. We further show that parametric spectral statistics for these systems are universal for small changes of the strength of the scatterer.