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