SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
Eigenstate thermalization in the Sachdev-Ye-Kitaev model
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abstract
The eigenstate thermalization hypothesis (ETH) explains how closed unitary quantum systems can exhibit thermal behavior in pure states. In this work we examine a recently proposed microscopic model of a black hole in AdS$_2$, the so-called Sachdev-Ye-Kitaev (SYK) model. We show that this model satisfies the eigenstate thermalization hypothesis by solving the system in exact diagonalization. Using these results we also study the behavior, in eigenstates, of various measures of thermalization and scrambling of information. We establish that two-point functions in finite-energy eigenstates approximate closely their thermal counterparts and that information is scrambled in individual eigenstates. We study both the eigenstates of a single random realization of the model, as well as the model obtained after averaging of the random disordered couplings. We use our results to comment on the implications for thermal states of the dual theory, i.e. the AdS$_2$ black hole.
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Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.
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Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity
SYK disorder is shown to be an approximate unitary k-design for poly(N) k; under the planted-SYK hardness conjecture this yields gravitationally pseudorandom unitaries, implying cryptographic censorship in JT gravity with the regularized maximal geodesic length as distinguisher.
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Krylov Complexity
Krylov complexity is a canonical, parameter-independent measure of operator spreading that probes chaotic dynamics to late times and admits a geometric interpretation in holographic duals.