 NSFPAR ID:
 10356354
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 9
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A bstract We reconsider the problem of bounding higher derivative couplings in consistent weakly coupled gravitational theories, starting from general assumptions about analyticity and Regge growth of the Smatrix. Higher derivative couplings are expected to be of order one in the units of the UV cutoff. Our approach justifies this expectation and allows to prove precise bounds on the order one coefficients. Our main tool are dispersive sum rules for the Smatrix. We overcome the difficulties presented by the graviton pole by measuring couplings at small impact parameter, rather than in the forward limit. We illustrate the method in theories containing a massless scalar coupled to gravity, and in theories with maximal supersymmetry.more » « less

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The ultimate regularity of quantum mechanics creates a tension with the assumption of classical chaos used in many of our pictures of chemical reaction dynamics. Outoftimeorder correlators (OTOCs) provide a quantum analog to the Lyapunov exponents that characterize classical chaotic motion. Maldacena, Shenker, and Stanford have suggested a fundamental quantum bound for the rate of information scrambling, which resembles a limit suggested by Herzfeld for chemical reaction rates. Here, we use OTOCs to study model reactions based on a doublewell reaction coordinate coupled to anharmonic oscillators or to a continuum oscillator bath. Upon cooling, as one enters the tunneling regime where the reaction rate does not strongly depend on temperature, the quantum Lyapunov exponent can approach the scrambling bound and the effective reaction rate obtained from a population correlation function can approach the Herzfeld limit on reaction rates: Tunneling increases scrambling by expanding the state space available to the system. The coupling of a dissipative continuum bath to the reaction coordinate reduces the scrambling rate obtained from the earlytime OTOC, thus making the scrambling bound harder to reach, in the same way that friction is known to lower the temperature at which thermally activated barrier crossing goes over to the lowtemperature activationless tunneling regime. Thus, chemical reactions entering the tunneling regime can be information scramblers as powerful as the black holes to which the quantum Lyapunov exponent bound has usually been applied.

A<sc>bstract</sc> We use a combination of analytical and numerical methods to study outoftime order correlators (OTOCs) in the sparse SachdevYeKitaev (SYK) model. We find that at a given order of
N , the standard result for theq local, alltoall SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter,k . We present an algorithm to sum the diagrams at any given order of 1/ (kq )^{n}. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This tradeoff between the efficiency of the sparse model and consistent behavior at finiteN becomes more significant for larger values ofN . 
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