Fine-grained chaos in AdS_2 Gravity
Fine-grained chaos in AdS_2 Gravity
Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time $\widehat{u}_*$. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes $AdS_2$ gravity and the low-energy dynamics of the SYK model. We identify a particular set of $2k$-point functions, characterized as being both "maximally braided" and "k-OTO", which exhibit exponential growth until progressively longer timescales $\widehat{u}^{(k)}_* = (k-1)\widehat{u}_*$. We suggest an interpretation as scrambling of increasingly fine-grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.
hep-th, cond-mat.stat-mech, gr-qc, nlin.CD, quant-ph
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Rozali, Moshe
fc0eb0db-9735-41d1-b543-76f2be76d809
19 March 2018
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Rozali, Moshe
fc0eb0db-9735-41d1-b543-76f2be76d809
Abstract
Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time $\widehat{u}_*$. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes $AdS_2$ gravity and the low-energy dynamics of the SYK model. We identify a particular set of $2k$-point functions, characterized as being both "maximally braided" and "k-OTO", which exhibit exponential growth until progressively longer timescales $\widehat{u}^{(k)}_* = (k-1)\widehat{u}_*$. We suggest an interpretation as scrambling of increasingly fine-grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.
More information
Published date: 19 March 2018
Additional Information:
8 pages; v2: minor clarifications, typos, added refs
Keywords:
hep-th, cond-mat.stat-mech, gr-qc, nlin.CD, quant-ph
Identifiers
Local EPrints ID: 471244
URI: http://eprints.soton.ac.uk/id/eprint/471244
PURE UUID: d19acd4d-e1cf-4b33-b8e0-5b5216a1cfe9
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Date deposited: 01 Nov 2022 17:41
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Felix M. Haehl
Author:
Moshe Rozali
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