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Diagnosing Chaos Using Four-Point Functions in Two-Dimensional Conformal Field Theory
Open accessAbstract
We study chaotic dynamics in two-dimensional conformal field theory through out-of-time-order thermal correlators of the form $⟨W(t)VW(t)V⟩$. We reproduce holographic calculations similar to those of Shenker and Stanford, by studying the large $c$ Virasoro identity conformal block. The contribution of this block to the above correlation function begins to decrease exponentially after a delay of $\ensuremath{\sim}{t}_{*}\ensuremath{-}(\ensuremath{\beta}/2\ensuremath{\pi})\mathrm{log}{\ensuremath{\beta}}^{2}{E}_{w}{E}_{v}$, where ${t}_{*}$ is the fast scrambling time $(\ensuremath{\beta}/2\ensuremath{\pi})\mathrm{log}c$ and ${E}_{w},{E}_{v}$ are the energy scales of the $W,V$ operators.
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Cites
Chaos and quantum thermalization
Srednicki, M. (1994) · Physical Review E · doi:10.1103/physreve.50.888 · Cited by 3,175
Quantum statistical mechanics in a closed system
Deutsch, J. M. (1991) · Physical Review A · doi:10.1103/physreva.43.2046 · Cited by 2,860
Black holes as mirrors: quantum information in random subsystems
Hayden, P., & Preskill, J. (2007) · Journal of High Energy Physics · doi:10.1088/1126-6708/2007/09/120 · Cited by 1,332
Sekino, Y., & Susskind, L. (2008) · Journal of High Energy Physics · doi:10.1088/1126-6708/2008/10/065 · Cited by 1,112
Time evolution of entanglement entropy from black hole interiors
Hartman, T., & Maldacena, J. (2013) · Journal of High Energy Physics · doi:10.1007/jhep05(2013)014 · Cited by 761
Shenker, S. H., & Stanford, D. (2015) · Journal of High Energy Physics · doi:10.1007/jhep05(2015)132 · Cited by 604
Self-citationSusskind, L. (2016) · Fortschritte der Physik · doi:10.1002/prop.201500095 · Cited by 427
Holographic entanglement entropy from 2d CFT: heavy states and local quenches
Asplund, C. T., Bernamonti, A., Galli, F., & Hartman, T. (2015) · Journal of High Energy Physics · doi:10.1007/jhep02(2015)171 · Cited by 280
Cited by
Remarks on the Sachdev-Ye-Kitaev model
Maldacena, J., & Stanford, D. (2016) · Physical Review D · doi:10.1103/physrevd.94.106002 · Cited by 1,852
Self-citationJensen, K. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.111601 · Cited by 695
The spectrum in the Sachdev-Ye-Kitaev model
Polchinski, J., & Rosenhaus, V. (2016) · Journal of High Energy Physics · doi:10.1007/jhep04(2016)001 · Cited by 699
Shenker, S. H., & Stanford, D. (2015) · Journal of High Energy Physics · doi:10.1007/jhep05(2015)132 · Cited by 604
Self-citationOn the dynamics of near-extremal black holes
Nayak, P., Shukla, A., Soni, R. M., Trivedi, S. P., & Vishal, V. (2018) · Journal of High Energy Physics · doi:10.1007/jhep09(2018)048 · Cited by 206
Metadata
- Authors
- Roberts, D. A., & Stanford, D.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2015-09-22
- Volume
- 115
- Issue
- 13
- Pages
- 131603-131603
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1603380880
- Cited by
- 467
- References
- 8
- FWCI
- 22.46
- Type
- journal article
- Language
- en
- Open access
- green
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