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Abstract
A simple probe of chaos and operator growth in manybody quantum systems is the out of time ordered four point function. In a large class of local systems, the effects of chaos in this correlator build up exponentially fast inside the so called butterfly cone. It has been previously observed that the growth of these effects is organized along rays and can be characterized by a velocity dependent Lyapunov exponent, λ(v). We show that this exponent is bounded inside the butterfly cone as λ(v) ≤ 2πT (1 − v/v _{B}), where T is the temperature and v _{B} is the butterfly speed. This result generalizes the chaos bound of Maldacena, Shenker and Stanford. We study λ(v) in some examples such as two dimensional SYK models and holographic gauge theories, and observe that in these systems the bound gets saturated at some critical velocity v _{*}< v _{B}. In this sense, boosting a system enhances chaos. We discuss the connection to conformal Regge theory, where λ(v) is related to the spin of the leading large N Regge trajectory, and controls the four point function in an interpolating regime between the Regge and the light cone limit. Finally, we comment on the generalization of the chaos bound to boosted and rotating ensembles and clarify some recent results on this in the literature.
Original language  English 

Article number  186 
Number of pages  34 
Journal  JHEP 
Volume  2020 
Issue number  1 
DOIs  
Publication status  Published  29 Jan 2020 
Bibliographical note
35 pages, 15 figures. v2: published versionKeywords
 hepth
 condmat.statmech
 condmat.strel
 nlin.CD
 quantph
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Projects
 1 Active

SRP8: Strategic Research Programme: HighEnergy Physics at the VUB
D'Hondt, J., Van Eijndhoven, N., Craps, B., Buitink, S., D'Hondt, J., Van Eijndhoven, N. & Craps, B.
1/11/12 → 31/10/22
Project: Fundamental