  Previous studies have suggested a crossover from superdiffusive to normal
heat transport in one-dimensional (1D) anharmonic oscillator systems with a
double-well type interatomic interaction like $V(\xi)=-\xi^2/2+\xi^4/4$, when
the system temperature is varied. In order to better understand this unusual
manner of thermal transport, here we perform a direct dynamics simulation to
examine how the spreading processes of the three physical quantities, i.e., the
heat, the total energy and the momentum, would depend on temperature. We find
three main points that are worth noting: (i) The crossover from superdiffusive
to normal heat transport is well verified from a new perspective of heat
spread; (ii) The spreading of the total energy is found to be very distinct
from heat diffusion, especially that under some temperature regimes, energy is
strongly localized, while heat can be superdiffusive. So one should take care
to derive a general connection between the heat conduction and energy
diffusion; (iii) In a narrow range of temperatures, the spreading of momentum
implies clear unusual non-ballistic behaviors; however, such unusual transport
of momentum cannot be directly related to the normal transport of heat. An
analysis of phonons spectra suggests that one should also take the effects of
phonons softening into account. All of these results may provide insights into
establishing the connection between the macroscopic heat transport and the
underlying dynamics in 1D systems.
