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Geometric Phase Curvature Statistics

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Abstract

The probability distribution of the magnitude C of the curvature 2-form, that underlies the quantum geometric phase and the reaction force of geometric magnetism, is calculated for an ensemble of three-parameter Hamiltonians represented by the gaussian unitary ensemble of N × N matrices. The distributions are determined analytically: exactly for N = 2 and approximately for N ≥ 3, and compared with simulations. The distributions decay asymptotically as 1/C5/2; this is a consequence of the codimension of energy-level degeneracies in the ensemble.

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Author notes

  1. M. V. Berry and Pragya Shukla contributed equally to this work.

Authors and Affiliations

  1. H H Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK

    M. V. Berry

  2. Department of Physics, Indian Institute of Science, Kharagpur, WB, 721302, India

    Pragya Shukla

  3. Department of Physics, Indian Institute of Science, Kanpur, UP, 208016, India

    Pragya Shukla

Authors
  1. M. V. Berry
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  2. Pragya Shukla
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Correspondence to M. V. Berry.

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Communicated by Juerg Martin Froehlich.

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Berry, M.V., Shukla, P. Geometric Phase Curvature Statistics. J Stat Phys 180, 297–303 (2020). https://doi.org/10.1007/s10955-019-02400-6

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