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Statistical properties of chaotic wavefunctions in two and more dimensions

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Abstract.

Starting with Berry's hypothesis for fixed energy waves in a classically chaotic system, and casting it in a Green function form, we derive wavefunction correlations and density matrices for few or many particles. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as N↦∞. This arises through a little known asymptotic limit of Bessel functions. The Berry random wave hypothesis in many dimensions may be viewed as an alternative approach to quantum statistical mechanics, when extended to include constraints and potentials.

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Authors and Affiliations

  1. Department of Physics, Harvard University, Cambridge, MA, 02138, USA

    E. J. Heller

  2. Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA

    E. J. Heller & B. Landry

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  1. E. J. Heller
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  2. B. Landry
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Correspondence to E. J. Heller.

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Heller, E., Landry, B. Statistical properties of chaotic wavefunctions in two and more dimensions . Eur. Phys. J. Spec. Top. 145, 231–244 (2007). https://doi.org/10.1140/epjst/e2007-00159-x

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  • DOI: https://doi.org/10.1140/epjst/e2007-00159-x

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