Towards the fast scrambling conjecture
 Nima Lashkari,
 Douglas Stanford,
 Matthew Hastings,
 Tobias Osborne,
 Patrick Hayden
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Many proposed quantum mechanical models of black holes include highly nonlocal interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use LiebRobinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.
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 Title
 Towards the fast scrambling conjecture
 Journal

Journal of High Energy Physics
2013:22
 Online Date
 April 2013
 DOI
 10.1007/JHEP04(2013)022
 Online ISSN
 10298479
 Publisher
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Lattice Integrable Models
 M(atrix) Theories
 Black Holes
 Quantum Dissipative Systems
 Industry Sectors
 Authors

 Nima Lashkari ^{(1)}
 Douglas Stanford ^{(2)}
 Matthew Hastings ^{(3)} ^{(4)}
 Tobias Osborne ^{(5)}
 Patrick Hayden ^{(1)} ^{(6)} ^{(7)}
 Author Affiliations

 1. Department of Physics, McGill University, Rue University, Montreal, QC, Canada
 2. Stanford Institute for Theoretical Physics, Department of Physics, Stanford University, Via Pueblo Mall, Stanford, CA, U.S.A
 3. Department of Physics, Duke University, Durham, NC, U.S.A
 4. Microsoft Station Q, Elings Hall, Santa Barbara, CA, U.S.A
 5. Institut für Theoretische Physik, Appelstrasse, Hannover, Germany
 6. School of Computer Science, McGill University, Rue University, Montreal, QC, Canada
 7. Perimeter Institute for Theoretical Physics, Caroline Street, Waterloo, ON, Canada