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.
Hot wormholes and chaos dynamics in a two-coupled SYK model
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abstract
We study the dynamics of chaos across the phase transition in a 2-coupled Sachdev-Ye-Kitaev (SYK) model, with a focus on the unstable "hot wormhole" phase. Using the Schwinger-Keldysh formalism, we employ two non-equilibrium protocols that allow access to this phase, which is inaccessible through equilibrium simulations: one involves cooling the system via a coupling to a thermal bath, while in the other we periodically drive the coupling parameter between the two sides. We numerically compute the Lyapunov exponents of the hot wormhole for the two cases. Our results uncover a rich structure within this phase, including both thermal and non-thermal solutions. These behaviors are analyzed in detail, with partial insights provided by the Schwarzian approximation, which captures certain but not all aspects of the observed dynamics.
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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.