A bound on chaos
- 1.3k Downloads
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 λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.
Keywords1/N Expansion Black Holes AdS-CFT Correspondence
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- M.B. Hastings, Locality in quantum systems, arXiv:1008.5137.
- C. Dankert, R. Cleve, J. Emerson and E. Livine, Exact and approximate unitary 2-designs and their application to fidelity estimation, Phys. Rev. A 80 (2009) 012304 [quant-ph/0606161].
- A. Kitaev, Hidden Correlations in the Hawking Radiation and Thermal Noise, talk given at Fundamental Physics Prize Symposium, November 10, 2014.Google Scholar
- A. Kitaev, Stanford SITP seminars, November 11 and December 18, 2014.Google Scholar
- G. ’t Hooft, The black hole interpretation of string theory, Nucl. Phys. B 335 (1990) 138 [INSPIRE].
- T. Dray and G. ’t Hooft, The Gravitational Shock Wave of a Massless Particle, Nucl. Phys. B 253 (1985) 173 [INSPIRE].