The finite-N spectrum of the two coupled SYK model organizes into operator-size clusters that underlie the conformal towers, revival dynamics, and wormhole-black hole transition.
Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
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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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Size Operator and Spectral Clustering in the Two Coupled SYK Model
The finite-N spectrum of the two coupled SYK model organizes into operator-size clusters that underlie the conformal towers, revival dynamics, and wormhole-black hole transition.