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Universal spectral form factor for chaotic dynamics | | Stefan Heusler
; Sebastian Müller
; Petr Braun
; Fritz Haake
; | | Date: |
5 Sep 2003 | | Journal: | J. Phys. A: Math. Gen. 37, L31 (2004) DOI: 10.1088/0305-4470/37/3/L02 | | Subject: | Chaotic Dynamics | nlin.CD | | Abstract: | We consider the semiclassical limit of the spectral form factor $K( au)$ of fully chaotic dynamics. Starting from the Gutzwiller type double sum over classical periodic orbits we set out to recover the universal behavior predicted by random-matrix theory, both for dynamics with and without time reversal invariance. For times smaller than half the Heisenberg time $T_Hpropto hbar^{-f+1}$, we extend the previously known $ au$-expansion to include the cubic term. Beyond confirming random-matrix behavior 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 $ au$-expansion. | | Source: | arXiv, nlin.CD/0309022 | | Services: | Forum | Review | PDF | Favorites | |
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