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2021

A bound on energy dependence of chaos

Hashimoto, Koji, Murata, Keiju, Tanahashi, Norihiro et al.

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We conjecture a chaos energy bound, an upper bound on the energy dependence of the Lyapunov exponent for any classical/quantum Hamiltonian mechanics and field theories.

The conjecture states that the Lyapunov exponent $\lambda(E)$ grows no faster than linearly in the total energy $E$ in the high energy limit.
In other words, the exponent $c$ in $\lambda(E) \propto E^c \,(E\to\infty)$ satisfies $c\leq 1$.
This chaos energy bound stems from thermodynamic consistency of out-of-time-order correlators (OTOC's) and applies to any classical/quantum system with finite $N$ / large $N$ ($N$ is the number of degrees of freedom) under plausible physical conditions on the Hamiltonians.

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