Correlation Function Bootstrapping in Quantum Chaotic Systems

Abstract

We discuss a general and efficient approach for "bootstrapping" short-time correlation data in chaotic or complex quantum systems to obtain information about long-time dynamics and stationary properties, such as the local density of states. When the short-time data is sufficient to identify an individual quantum system, we obtain a systematic approximation for the spectrum and wave functions. Otherwise, we obtain statistical properties, including wave function intensity distributions, for an ensemble of all quantum systems sharing the given short-time correlations. The results are valid for open or closed systems, and are stable under perturbation of the short-time input data. Numerical examples include quantum maps and two-dimensional anharmonic oscillators.

19 pages, including 10 figures, submitted to Phys. Rev. E

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Cited by in corpus (6)

• Characterization of random features of chaotic eigenfunctions in unperturbed basis
• A Method to Modify RMT using Short-Time Behavior in Chaotic Systems
• Statistical distribution of components of energy eigenfunctions: from nearly-integrable to chaotic
• Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices
• Convergent perturbation expansion of energy eigenfunctions on unperturbed basis states in classically-forbidden regions
• Integrating Random Matrix Theory Predictions with Short-Time Dynamical Effects in Chaotic Systems