Journal
PHYSICAL REVIEW E
Volume 99, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.99.052212
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Funding
- Gordon and Betty Moore Foundation, under the EPiQS initiative, at the Kavli Institute for Theoretical Physics [GBMF4304]
- Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC [DMR-1720256]
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We view the operator spreading in chaotic evolution as a stochastic process of height growth. The height of an operator represents the size of its support and chaotic evolution increases the height. We consider N-spin models with all two-body interactions and embody the height picture in a random model. The exact solution shows that the mean height, being proportional to the squared commutator, grows exponentially within log N scrambling time and saturates in a manner of logistic function. We propose that the temperature dependence of the chaos bound could be due to initial height biased toward high operators, which has a smaller Lyapunov exponent.
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