Hot wormholes and chaos dynamics in a two-coupled SYK model

TL;DR

This paper investigates chaos and phase transitions in a two-coupled SYK model, revealing complex hot wormhole dynamics through non-equilibrium protocols and numerical Lyapunov exponent calculations.

Contribution

It introduces two novel non-equilibrium protocols to access the hot wormhole phase and analyzes chaos dynamics beyond equilibrium methods.

Findings

Identification of rich structure within the hot wormhole phase

Numerical computation of Lyapunov exponents for different protocols

Partial insights from Schwarzian approximation

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.