title: A review of sigma models for quantum chaotic dynamics.
abstract: We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization.
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Deutschland.
authors.forename: Alexander
authors.initials: A
authors.lastname: Altland
authors.forename: Sven
authors.initials: S
authors.lastname: Gnutzmann
authors.forename: Fritz
authors.initials: F
authors.lastname: Haake
authors.forename: Tobias
authors.initials: T
authors.lastname: Micklitz
mesh_terms: D003196:Computer Graphics; D017711:Nonlinear Dynamics; D011789:Quantum Theory