Quantum complexity and negative curvature

Brown, Adam R.; Susskind, Leonard; Zhao, Ying

doi:10.1103/physrevd.95.045010

Cited by 160 publications

(268 citation statements)

References 21 publications

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“…The upper bound is given by the surface gravity of the horizon, (27), and in particular is independent of the forces which pull the particle not to fall into the horizon. The separatrix is located very near the horizon.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The bound is saturated by the Sachdev-Ye-Kitaev model [11,12], which ignited interesting development (see for example [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], and also [33][34][35][36][37][38][39][40][41][42][43][44][45][46]). One of the important questions is, among various physics associated with black hole horizons, what provides the bound, other than the shock waves.…”

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confidence: 99%

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Universality in chaos of particle motion near black hole horizon

2017

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Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, the Lyapunov exponent is subject to an inequality λ ≤ 2πTBH/ , which is identical to the bound recently discovered by Maldacena, Shenker and Stanford.

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Section: Conclusion and Discussionmentioning

confidence: 99%

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confidence: 99%

Universality in chaos of particle motion near black hole horizon

2017

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“…It has a similar property to entropy as an increasing function of time [139,140,141]. Complexity in de Sitter space or negative curvature is studied in [43,94]. The action calculation for some cases includes divergence because of the AdS boundary [142,143].…”

Section: Introductionmentioning

confidence: 99%

Complexity growth of rotating black holes with a probe string

Nagasaki

2018

Phys. Rev. D

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We consider the growth of the action for black hole spacetime with a fundamental string. According to "complexity -action" conjecture it is expected to be equal to complexity which describes the quantum states of black holes. We consider black holes with three different horizon topologies. These have positive, negative and zero curvatures. We are interested in the complexity growth of these system with a fundamental string. We find that for the case where the black holes have the toroidal horizon structure the probe string behaves very differently from the other two cases.

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“…[27][28][29][30][31]) and the gravity action in Wheeler-De Witt patch in [32,33] (for recent progresses see e.g. [34][35][36][37][38][39][40][41][42]). We would also like to mention that for CFTs, the behavior of the complexity is very similar to the quantum information metric under marginal deformations as pointed out in [43] (refer to [27,31,44] for recent developments), where the metric is argued to be well approximated by the volume of maximal time slice in AdS.…”

Section: Jhep11(2017)097mentioning

confidence: 99%

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

282

402

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Abstract:We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

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Quantum complexity and negative curvature

Cited by 160 publications

References 21 publications

Universality in chaos of particle motion near black hole horizon

Universality in chaos of particle motion near black hole horizon

Complexity growth of rotating black holes with a probe string

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

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