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Chaos in QFT

Nadav Shrayer* and Jacob Sonnenschein†

  • The Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel

  • *Contact author: nadavshraier@tauex.tau.ac.il
  • †Contact author: cobi@tauex.tau.ac.il
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Phys. Rev. D 113, 105021 – Published 26 May, 2026

DOI: https://doi.org/10.1103/n1nn-v3ny

Abstract

In this paper we explore the chaotic behavior of nonintegrable quantum field theories and compare them to integrable ones. We choose as prototypes the double sine-Gordon and the sine-Gordon models. We analyze their discrete spectrum determined by a truncation method. We examine the map of the corresponding energy eigenvalues to the eigenvalues of the random matrix theory Gaussian orthogonal ensemble (GOE). This is done by computing the following properties: (a) The distribution of the adjacent spacings and their ratios, (b) higher order spacings and ratios, (c) pair correlations, (d) spectral form factors, and (e) spectral rigidity. For these properties we determine the differences between the integrable and nonintegrable theories and verify that the former admits a Poisson behavior and the latter GOE (apart from the spectral rigidity, which shows mixed behavior).

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Phys. Rev. D 113, 105021– Published 26 May, 2026
  • Received 28 January 2026
  • Accepted 27 April 2026
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