Sigma models for quantum chaotic dynamics
arXiv:1412.5336 · doi:10.1088/0034-4885/78/8/086001
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.
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Cited by in corpus (8)
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- Universal level statistics of the out-of-time-ordered operator
- Probing the topological Anderson transition with quantum walks
- Quantum Hall criticality in Floquet topological insulators
- Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops
- Self-duality triggered dynamical transition
- Effective field theory of random quantum circuits
- Statistics of the Random Matrix Spectral Form Factor