Periodic-Orbit Theory of Universality in Quantum Chaos

Simple item page
dc.creatorMüller, Sebastian
dc.creatorHeusler, Stefan
dc.creatorBraun, Petr
dc.creatorHaake, Fritz
dc.creatorAltland, Alexander
dc.date2005-03-23
dc.date.accessioned2026-07-07T06:34:16Z
dc.date.available2026-07-07T06:34:16Z
dc.descriptionWe argue semiclassically, on the basis of Gutzwiller's periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-Dyson symmetry classes, we calculate the small-time spectral form factor $K(τ)$ as power series in the time $τ$. Each term $τ^n$ of that series is provided by specific families of pairs of periodic orbits. The contributing pairs are classified in terms of close self-encounters in phase space. The frequency of occurrence of self-encounters is calculated by invoking ergodicity. Combinatorial rules for building pairs involve non-trivial properties of permutations. We show our series to be equivalent to perturbative implementations of the non-linear sigma models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs are one-to-one with Feynman diagrams known from the sigma model.
dc.description31 pages, 17 figures
dc.identifierhttps://arxiv.org/abs/nlin/0503052
dc.identifierhttp://arxiv.org/abs/nlin/0503052
dc.identifierPhys. Rev. E 72, 046207 (2005)
dc.identifierdoi:10.1103/PhysRevE.72.046207
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99475
dc.subjectChaotic Dynamics
dc.subjectMesoscale and Nanoscale Physics
dc.titlePeriodic-Orbit Theory of Universality in Quantum Chaos
dc.typetext

Files

Collections

arXiv