Fast scramblers

Sekino, Yasuhiro; Susskind, Leonard

doi:10.1088/1126-6708/2008/10/065

Cited by 1,079 publications

(1,535 citation statements)

References 15 publications

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“…5 Among other places, this fact was discussed in the works [70][71][72] in relation to the consistency between black hole complementarity and the absence of quantum cloning. This geometric-optics observation can easily be extrapolated to classical wave mechanics.…”

Section: Collapsing Stars and Eternal Black Holesmentioning

confidence: 99%

An infalling observer in AdS/CFT

Papadodimas

Raju

2013

J. High Energ. Phys.

346

593

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We describe the experience of an observer falling into a black hole using the AdS/CFT correspondence. In order to do this, we reconstruct the local bulk operators measured by the observer along his trajectory outside the black hole. We then extend our construction beyond the black hole horizon. We show that this is possible because of an effective doubling of the observables in the boundary theory, when it is in a pure state that is close to the thermal state. Our construction allows us to rephrase questions about information-loss and the structure of the metric at the horizon in terms of more familiar CFT correlators. It suggests that to precisely identify black-hole microstates, the observer would need to conduct measurements to an accuracy of e −S BH . This appears to be inconsistent with the "fuzzball" proposal, and other recent proposals in which pure states in the ensemble of the black hole are represented by macroscopically distinct geometries. Furthermore, our description of the black hole interior in terms of CFT operators provides a natural realization of black hole complementarity and a method of preserving unitarity without "firewalls."

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Section: Collapsing Stars and Eternal Black Holesmentioning

confidence: 99%

An infalling observer in AdS/CFT

Papadodimas

Raju

2013

J. High Energ. Phys.

346

593

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“…For more details, we refer to [15,19,[37][38][39][40][41][42][43]. The butterfly effect as chaotic behaviour refers to the exponential growth of a small perturbation to a quantum system.…”

Section: Butterfly Velocitymentioning

confidence: 99%

Diffusion and butterfly velocity at finite density

Niu

Kim

2017

J. High Energ. Phys.

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Abstract:We study diffusion and butterfly velocity (v B ) in two holographic models, linear axion and axion-dilaton model, with a momentum relaxation parameter (β) at finite density or chemical potential (µ). Axion-dilaton model is particularly interesting since it shows linear-T -resistivity, which may have something to do with the universal bound of diffusion. At finite density, there are two diffusion constants D ± describing the coupled diffusion of charge and energy. By computing D ± exactly, we find that in the incoherent regime (β/T 1, β/µ 1) D + is identified with the charge diffusion constant (D c ) and D − is identified with the energy diffusion constant (D e ). In the coherent regime, at very small density, D ± are 'maximally' mixed in the sense that D + (D − ) is identified with D e (D c ), which is opposite to the case in the incoherent regime. In the incoherent regime D e ∼ C − v 2 B /k B T where C − = 1/2 or 1 so it is universal independently of β and µ. However, D c ∼ C + v 2 B /k B T where C + = 1 or β 2 /16π 2 T 2 so, in general, C + may not saturate to the lower bound in the incoherent regime, which suggests that the characteristic velocity for charge diffusion may not be the butterfly velocity. We find that the finite density does not affect the diffusion property at zero density in the incoherent regime.

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“…The entanglement entropy, and even its time dependence, is also beginning to be experimentally measurable in cold atom systems [32][33][34]. In a very different context, black holes have motivated studies of how fast quantum systems can scramble information by dynamically generating entanglement [35][36][37][38]. Simple quantum circuitsquantum evolutions in discrete time-serve as useful toy models for entanglement growth and scrambling [39][40][41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Quantum Entanglement Growth under Random Unitary Dynamics

et al. 2017

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Characterizing how entanglement grows with time in a many-body system, for example, after a quantum quench, is a key problem in nonequilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing either Hamiltonian evolution with time-dependent noise or evolution by a random quantum circuit. Our results reveal a universal structure behind noisy entanglement growth, and also provide simple new heuristics for the "entanglement tsunami" in Hamiltonian systems without noise. In 1D, we show that noise causes the entanglement entropy across a cut to grow according to the celebrated KardarParisi-Zhang (KPZ) equation. The mean entanglement grows linearly in time, while fluctuations grow like ðtimeÞ 1=3 and are spatially correlated over a distance ∝ ðtimeÞ 2=3 . We derive KPZ universal behavior in three complementary ways, by mapping random entanglement growth to (i) a stochastic model of a growing surface, (ii) a "minimal cut" picture, reminiscent of the Ryu-Takayanagi formula in holography, and (iii) a hydrodynamic problem involving the dynamical spreading of operators. We demonstrate KPZ universality in 1D numerically using simulations of random unitary circuits. Importantly, the leading-order time dependence of the entropy is deterministic even in the presence of noise, allowing us to propose a simple coarse grained minimal cut picture for the entanglement growth of generic Hamiltonians, even without noise, in arbitrary dimensionality. We clarify the meaning of the "velocity" of entanglement growth in the 1D entanglement tsunami. We show that in higher dimensions, noisy entanglement evolution maps to the wellstudied problem of pinning of a membrane or domain wall by disorder.

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Fast scramblers

Cited by 1,079 publications

References 15 publications

An infalling observer in AdS/CFT

An infalling observer in AdS/CFT

Diffusion and butterfly velocity at finite density

Quantum Entanglement Growth under Random Unitary Dynamics

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