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arXiv · 2602.07952

Higher-Order Corrections to Scrambling Dynamics in Brownian Spin SYK Models

Tingfei Li·Miao Wang·Jianghui Yu
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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 interactions of order two up to $L$, 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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Tingfei Li, Miao Wang, Jianghui Yu. 2026-02-08. Higher-Order Corrections to Scrambling Dynamics in Brownian Spin SYK Models. https://arxiv.org/abs/2602.07952

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