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On the relation between the magnitude and exponent of OTOCs · Around

2018

On the relation between the magnitude and exponent of OTOCs

Gu, Yingfei, Kitaev, Alexei

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We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called "branching time".

The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel.
This identity can be used to calculate stringy effects in the SYK and similar models, we also explicitly define "strings" in this context.
As another application, we consider an SYK chain.

Built on

A. I. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity http://www.jetp.ac.ru/cgi-bin/e/index/e/28/6/p1200?a=list , Soviet Physics, JETP 28
1969
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S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet , Phys. Rev. Lett. 70
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S. H. Shenker and D. Stanford, Stringy effects in scrambling , JHEP 05
Original
2015
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A. Kitaev, “Hidden correlations in the Hawking radiation and thermal noise.” Talk at KITP http://online.kitp.ucsb.edu/online/joint98/kitaev/ , February, 2015
2015
Earlier work this paper cites.
A. Kitaev, “A simple model of quantum holography.” Talks at KITP http://online.kitp.ucsb.edu/online/entangled15/kitaev/ and http://online.kitp.ucsb.edu/online/entangled15/kitaev2/ , April and May, 2015
2015
Earlier work this paper cites.

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Then

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D. Stanford and D. Simmons-Duffin. Private communication

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