A review of sigma models for quantum chaotic dynamics. (16th July 2015)

• Record Type: Journal Article
• Authors: Altland, Alexander; Gnutzmann, Sven; Haake, Fritz; Micklitz, Tobias
• Is Part Of: Reports on progress in physics. Volume 78:Number 8(2015:Aug.)
• Publication Date: 2015-07-16
• Subjects: quantum chaos -- nonlinear dynamics -- field theory; Physics -- Periodicals; 530.05
• DOI: 10.1088/0034-4885/78/8/086001
• Languages: English
• ISSNs: 0034-4885

Abstract

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.