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Operator Size Distribution in Large N Quantum Mechanics of Majorana Fermions

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arxiv 2212.04358 v1 pith:SDYCMDV4 submitted 2022-12-08 cond-mat.str-el hep-thquant-ph

Operator Size Distribution in Large N Quantum Mechanics of Majorana Fermions

classification cond-mat.str-el hep-thquant-ph
keywords largeoperatorquantumsizedistributionevolutionfermionsmajorana
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Under the Heisenberg evolution in chaotic quantum systems, initially simple operators evolve into complicated ones and ultimately cover the whole operator space. We study the growth of the operator ``size'' in this process, which is related to the out-of-time-order correlator (OTOC). We derive the full time evolution of the size distribution in large $N$ quantum mechanics of Majorana fermions. As examples, we apply the formalism to the Brownian SYK model (infinite temperature) and the large $q$ SYK model (finite temperature).

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

    quant-ph 2026-02 conditional novelty 6.0

    Operator growth in Brownian spin SYK is solved beyond leading order with a generating-function 1/N perturbation theory; higher-order corrections set the late-time universal (two-body) and parity-protected (three-body)...