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arXiv · 2212.04358

Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions

Pengfei Zhang·Yingfei Gu
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Abstract

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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Pengfei Zhang, Yingfei Gu. 2022-12-08. Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions. https://doi.org/10.1007/jhep10(2023)018

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