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Cornering the universal shape of fluctuations

Author

Listed:
  • Benoit Estienne

    (Laboratoire de Physique Théorique et Hautes Énergies, LPTHE)

  • Jean-Marie Stéphan

    (Institut Camille Jordan)

  • William Witczak-Krempa

    (Université de Montréal
    Université de Montréal
    Regroupement Québécois sur les Matériaux de Pointe (RQMP))

Abstract

Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations in a subregion of the full system, focusing on geometries with sharp corners. We report that the angle dependence is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We exemplify our findings with fractional quantum Hall states, topological insulators, scale invariant quantum critical theories, and metals. We suggest experimental tests, and anticipate that our findings can be generalized to other spatial dimensions or geometries. In addition, we highlight the similarities of the fluctuation shape dependence with findings relating to quantum entanglement measures.

Suggested Citation

  • Benoit Estienne & Jean-Marie Stéphan & William Witczak-Krempa, 2022. "Cornering the universal shape of fluctuations," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-021-27727-1
    DOI: 10.1038/s41467-021-27727-1
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