We find that localised perturbations in a chaotic classical many-body
system-- the classical Heisenberg We find that the effects of a localised
perturbation in a chaotic classical many-body system--the classical Heisenberg
chain at infinite temperature--spread ballistically with a finite speed even
when the local spin dynamics is diffusive. We study two complementary aspects
of this butterfly effect: the rapid growth of the perturbation, and its
simultaneous ballistic (light-cone) spread, as characterised by the Lyapunov
exponents and the butterfly speed respectively. We connect this to recent
studies of the out-of-time-ordered commutators (OTOC), which have been proposed
as an indicator of chaos in a quantum system. We provide a straightforward
identification of the OTOC with a natural correlator in our system and
demonstrate that many of its interesting qualitative features are present in
the classical system. Finally, by analysing the scaling forms, we relate the
growth, spread and propagation of the perturbation with the growth of
one-dimensional interfaces described by the Kardar-Parisi-Zhang (KPZ) equation.Comment: 6 pages, 6 figures. Journal Ref. added: Physical Review Letters 121,
024101 (2018
