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Pair correlations of quantum chaotic maps from supersymmetry
Martin R. Zirnbauer
A conjecture due to Bohigas, Giannoni and Schmit (BGS), stating that the energy level correlations of quantum chaotic systems generically obey the laws of random matrix theory, is…
The color-flavor transformation and a new approach to quantum chaotic maps
Martin R. Zirnbauer
The color-flavor transformation is a mathematical result that has applications to problems as diverse as lattice gauge theory, random network models, and dynamical systems. Several…
Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
Martin R. Zirnbauer
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introdu…
Field theory of the quantum kicked rotor
Alexander Altland, Martin R. Zirnbauer
The quantum kicked rotor is investigated by field theoretical methods. It is shown that the effective theory describing the long wave length physics of the system is precisely the…