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Title
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Semiclassical echo dynamics in the Sachdev-Ye-Kitaev model
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Author
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Abstract
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| The existence of a quantum butterfly effect in the form of exponential sensitivity to small perturbations has been under debate for a long time. Lately, this question has gained increased interest due to the proposal to probe chaotic dynamics and scrambling using out-of-time-order correlators. In this work we study echo dynamics in the Sachdev-Ye-Kitaev model under effective time reversal in a semiclassical approach using the truncated Wigner approximation, which accounts for nonvanishing quantum fluctuations that are essential for the dynamics. We demonstrate that small imperfections introduced in the time-reversal procedure result in an exponential divergence from the perfect echo, which allows us to identify a Lyapunov exponent lambda(L). In particular, we find that lambda(L) is twice the Lyapunov exponent of the semiclassical equations of motion. This behavior is attributed to the growth of an out-of-time-order double commutator that resembles an out-of-time-order correlator. |
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Language
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English
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Source (journal)
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Physical review B / American Physical Society. - New York, N.Y, 2016, currens
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Publication
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New York, N.Y
:
American Physical Society
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2019
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ISSN
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2469-9969
[online]
2469-9950
[print]
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DOI
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10.1103/PHYSREVB.99.134301
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Volume/pages
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99
:13
(2019)
, 10 p.
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Article Reference
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134301
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ISI
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000463880300002
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Medium
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E-only publicatie
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Full text (Publisher's DOI)
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Full text (open access)
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