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Page curves and replica wormholes from random dynamics
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We show how to capture both the non-unitary Page curve and replica wormhole-like contributions that restore unitarity in a toy quantum system with random dynamics. The motivation is to find the simplest dynamical model that captures this aspect of gravitational physics. In our model, we evolve with an ensemble of Hamiltonians with GUE statistics within microcanonical windows. The entropy of the averaged state gives the non-unitary curve, the averaged entropy gives the unitary curve, and the difference comes from matrix index contractions in the Haar averaging that connect the density matrices in a replica wormhole-like manner.
Forward citations
Cited by 2 Pith papers
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Islands, Double Holography, and the Entanglement Membrane
A double-holographic Page curve is realized as an entanglement membrane with a vertical growing segment before the Page time and two saturated butterfly-velocity lines exiting through a boundary after it.
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