Bound on energy dependence of chaos

نویسندگان

چکیده

We conjecture a chaos energy bound, an upper bound on the dependence of Lyapunov exponent for any classical/quantum Hamiltonian mechanics and field theories. The states that $\ensuremath{\lambda}(E)$ grows no faster than linearly in total $E$ high limit. In other words, $c$ $\ensuremath{\lambda}(E)\ensuremath{\propto}{E}^{c}(E\ensuremath{\rightarrow}\ensuremath{\infty})$ satisfies $c\ensuremath{\le}1$. This stems from thermodynamic consistency out-of-time-order correlators applies to system with finite $N/\mathrm{large}$ $N$ ($N$ is number degrees freedom) under plausible physical conditions Hamiltonians. To best our knowledge satisfied by classically chaotic known, consistent cerebrated Maldacena, Shenker, Stanford, which quantum cases at large $N$. provide arguments supporting generic billiards multiparticle systems. existence may put fundamental constraint systems Universe.

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ژورنال

عنوان ژورنال: Physical review

سال: 2022

ISSN: ['0556-2813', '1538-4497', '1089-490X']

DOI: https://doi.org/10.1103/physrevd.106.126010