A bound on chaos

By J. Maldacena, S. Shenker, D. Stanford. Journal of High Energy Physics, 2015

2,328 citations recorded by the source corpus.

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λL ≤ 2πkBT/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8bf5023b41fa290d5054efd7e92bb3630e22ba1c

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Citations in the corpus

Random Quantum Circuits (2022, methodology): “The evolution of local observables also exhibits universal structure, for example in the decay of correlations and in the process of “scrambling”, where information that is initially stored locally becomes delocalized (165, 166, 167).”
Quantum Butterfly Effect in Weakly Interacting Diffusive Metals (2017, background): “By considering an appropriate analytic continuation of f(t), one can show that there is a fundamental upper bound on λL(≤ 2πkBT/~) [21]; black-holes and certain random fermion models [18, 22] saturate the bound.”
Scrambling Dynamics and Out-of-Time-Ordered Correlators in Quantum Many-Body Systems (2022, background): “The chaos bound [11] concerns a finite temperature version of the OTOC and shows that λL < 2πT in a quite general setting, leading to extensive studies on understanding and refining the bound and on operator growth in general, especially at finite temperature, e.”
A Universal Operator Growth Hypothesis (2018, methodology): “This suggests that an extension of the bound λL ≤ 2α to finite temperature can be obtained by comparing the finite-T Lyapunov exponent (as defined in [12]) and the finite-T growth rate defined with the Wightman inner product:”
Complexity, action, and black holes (2015, background): “thmic in N, they also have the smallest possible coecient in front of the logarithm t = 1 L logN; (2.5) where the rate of scrambling can be interpreted in terms of chaos as a Lyapunov exponent L [24,27]. A useful measure of the strength of chaos is given by the out-oftime-order four-point correlat”
Locality, Quantum Fluctuations, and Scrambling (2018, background): “On the other hand, at finite temperature and assuming a separation of timescales, there is a thermally regulated version of the OTOC whose growth rate is bounded by the temperature [58].”
Chaos, complexity, and random matrices (2017, background): “In strongly chaotic large-N systems, we expect the following behaviors [6, 9]:”
A proof of the conformal collider bounds (2016, background): “ CFT unitarity/re ection positivity implies both causality and sum rules leading to constraints on the signs of products of OPE coecients. These constraints are closely related to the bound on chaos [30,31] as discussed in the context of CFT correlators in [32{35]. The argument was made for scalar 4”
Bounding the space of holographic CFTs with chaos (2016, methodology): “We also note the imaginary time parameterization used in [2],”
Causality constraints in conformal field theory (2015, methodology): “Relation to the chaos bound Our derivation is closely related to the bound on chaos recently derived in [41] (see also [54–56]).”
Entanglement Membrane in Chaotic Many-Body Systems (2019, methodology): “[26] Juan Maldacena, Stephen H.”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, background): “More recent work has related holographic behavior to polynomial boundedness of Mellin amplitudes [40,41], and to the onset of chaos in thermal quantum systems [42].”