Chaos in AdS$_2$ holography

Jensen, Kristan

doi:10.48550/arxiv.1605.06098

Cited by 151 publications

(301 citation statements)

References 22 publications

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“…8 To the best of our knowledge this relation is still unproven for Schwarzschild black holes. 9 With the constraint that we are only interested in states that evolve to the same thermal state.…”

Section: Resultsmentioning

confidence: 99%

“…In recent years OTOCs and these exponents, encoding the speed with which quantum systems scramble information, received much attention [9][10][11][12][13][14][15], especially after it was shown that there exists an upper bound [1] for λ OTOC ≤ 2πT and thus an upper bound on the speed of the development of quantum chaos. Furthermore, systems that are holographic duals to Einstein gravity have been found to saturate this bound [1,5,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

Maier,

Schäfer,

Waeber

2021

Preprint

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In classical chaotic systems the entropy, averaged over initial phase space distributions, follows an universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the Kolmogorov-Sinai entropy, is given by the sum over all positive Lyapunov exponents. A natural question is whether a similar relation is valid for quantum systems. We argue that the Maldacena-Shenker-Stanford bound on quantum Lyapunov exponents λ implies that the upper bound on the growth rate of the entropy, averaged over states in Hilbert space that evolve towards a thermal state with temperature T and entropy S eq , should be given by S eq πT = λ>0 2πT . Strongly coupled, large N theories with black hole duals should saturate the bound. By studying a large number of isotropization processes of random, spatially homogeneous, far from equilibrium initial states in large N , N = 4 Super Yang Mills theory at strong coupling and computing the ensemble averaged growth rate of the dual black hole's apparent horizon area, we find both an analogous behavior as in classical chaotic systems and numerical evidence that the conjectured bound on averaged entropy growth is saturated granted that the Lyapunov exponents are degenerate λ = ±2πT . This fits to the behavior of classical systems with plus/minus symmetric Lyapunov spectra, a symmetry which implies the validity of Liouville's theorem.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

Maier,

Schäfer,

Waeber

2021

Preprint

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“…However, in order to be clear about the problem that we want to address, we need to recall some aspects of the SYK model. In particular, it is well known that the infrared theory in the strong coupling limit is described by hydrodynamics [66]. In § 3.1, we first briefly review the model.…”

Section: The Modelmentioning

confidence: 99%

Long-time tails in the SYK chain from the effective field theory with a large number of derivatives

Abbasi

2021

Preprint

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We study the nonlinear energy diffusion through the SYK chain in the framework of Schwinger-Keldysh effective field theory. We analytically construct the interacting effective Lagrangian up to 40 th order in the derivative expansion. According to this effective Lagrangian, we calculate the first order loop correction of the energy density response function, the pole of which is the dispersion relation of energy diffusion. As expected, we see that the standard derivative expansion of that dispersion relation,), breaks down due to the long-time tails. However, we find that the nonlinear contribution of order n to the self-energy is proportional to k 2 n+1/2 . This suggests to modify the dispersion relation by splitting it into two dispersion relations and double the number of transport coefficients at any order as). We find that the modified series, which include the effect of long-time tails, are convergent. The radius of convergence is proportional to the ratio of thermal conductivity to diffusion constant.

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“…The path integral in the JT gravity on Riemann surfaces with asymptotic boundaries is obtained by computing the path integral over the wiggles along the asymptotic boundaries of the surfaces [30,31,32], together with the path integral over the moduli of the Riemann surfaces with the geodesic boundaries and the path integral over the "trumpets" connecting an asymptotic boundary (with which a boundary wiggle is associated) and a geodesic boundary [8]. The volume of the moduli of hyperbolic Riemann surfaces with geodesic boundaries is known as the "Weil-Petersson volume.…”

Section: Introductionmentioning

confidence: 99%

Path integrals in JT gravity and Virasoro constraints

Kimura

2021

Preprint

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We compute the higher-genus contributions to the correlation functions in Jackiw-Teitelboim gravity, by utilizing the large-g asymptotics of the Weil-Petersson volumes as functions of genus g and the number of boundaries, n, obtained in a previous study. We also compute the higher-genus contributions to resolvents on the matrix-integral side for any n number of boundaries of the Riemann surfaces. Further, we compute the intersection numbers on the moduli space of the Riemann surfaces of large genera with any n number of boundaries, focusing on the cases with two or more boundaries (n ≥ 2).

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Chaos in AdS$_2$ holography

Cited by 151 publications

References 22 publications

Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

Long-time tails in the SYK chain from the effective field theory with a large number of derivatives

Path integrals in JT gravity and Virasoro constraints

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