From quantum disorder to quantum chaos

Abstract

We study the statistics of wave functions in a ballistic chaotic system. The statistical ensemble is generated by adding weak smooth random potential, which allows us to apply the ballistic $\sigma$-model approach. We analyze conditions of applicability of the $\sigma$-model, emphasizing the role played by the single-particle mean free path and the Lyapunov exponent due to the random potential. In particular, we present a resolution of the puzzle of repetitions of periodic orbits counted differently by the $\sigma$-model and by the trace formula.

15 pages, no figures. Contribution to a special issue of J. Low Temp. Phys. dedicated to Peter Woelfle's 60th birthday

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Cited by in corpus (12)

• Interaction-induced magnetoresistance in a two-dimensional electron gas
• Loschmidt Echo and Lyapunov Exponent in a Quantum Disordered System
• The Ehrenfest Oscillations in The Level Statistics of Chaotic Quantum Dots
• From quantum disorder to quantum chaos
• Spin and interaction effects in quantum dots: a Hartree-Fock-Koopmans approach
• Non-linear $\sigma$-model for long range disorder and quantum chaos
• Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces
• Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model
• Spin and orbital effects in a 2D electron gas in a random magnetic field
• Ballistic electron motion in a random magnetic field
• Brownian Motion Model of Quantization Ambiguity and Universality in Chaotic Systems
• Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Dynamical Effects