  The traditional picture of heat transfer in solids by atomic vibrations, also
known as phonons, involves phonons scattering with each other like gas
particles and is commonly referred to as the phonon gas model (PGM). This
physical picture accounts for interactions among propagating (i.e., plane wave
modulated) vibrational modes in an ideal crystal, but it becomes problematic
when describing non-propagating modes arising in realistic non-idealized
systems. Here, we introduce a more general formalism for studying phonon
transport, which involves projection of the interatomic interactions themselves
(i.e., not just the atom motion), onto the normal modes of the system. This
shows, for the first time, how energy is exchanged between modes in real-time
during molecular dynamics (MD) simulations, as opposed to other MD methods
which use inferences based on correlations, or other time averaged schemes that
do not preserve specific features in the real-time dynamics. Applying this
formalism to the example case of modes interacting in a superlattice, we
illustrate a new perspective on how phonon transport occurs, whereby individual
normal modes share energy through specific channels of interaction with other
modes. We also highlight that while a myriad of interaction pathways exist,
only a tiny fraction of these pathways actually transfer significant amounts of
energy, which is surprising. The approach allows for the prediction and
simulation of these mode/phonon interactions, thus unveiling the real-time
dynamics of phonon behavior and advancing our ability to understanding and
engineer phonon transport.
