Universal spectral correlations from the ballistic sigma model
arXiv:0707.2274 · doi:10.1103/PhysRevE.76.056204
Abstract
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of quantum interference in chaotic systems and show how semiclassical 'diagrams' involving near action degenerate sets of periodic orbits emerge in the field theoretical description. We further discuss how the universality phenomenon (i.e. the fact that individual chaotic systems behave according to the prescriptions of random matrix theory) can be understood from the perspective of the field theory.
10 pages, 3 figures
References in corpus (6)
- Semiclassical Foundation of Universality in Quantum Chaos
- Periodic-Orbit Theory of Universality in Quantum Chaos
- Periodic-Orbit Theory of Level Correlations
- Universal spectral form factor for chaotic dynamics
- The spectral form factor near the Ehrenfest-time
- Field Theory Approach to Quantum Interference in Chaotic Systems