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

• URL: http://arxiv.org/abs/2602.07952v1
• Date: Sun, 08 Feb 2026 12:50:53 GMT
• Title: Higher-Order Corrections to Scrambling Dynamics in Brownian Spin SYK Models
• Abstract summary: We investigate operator growth in a Brownian spin Sachdev--Ye--Kitaev (SYK) model with random all-to-all interactions.<n>For Hamiltonians containing interactions of order two up to $L$, we derive a closed master equation for the Pauli-string expansion coefficients.<n>We show 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.
• Score: 5.091861856964667
• License: http://creativecommons.org/licenses/by/4.0/
• 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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