Sub-Planckian thermal diffusivity in a classical model with lattice dynamics

Planckian transport, characterized by a relaxation timescale of τ_H=hbar/k_BT, has been suggested to appear in many correlated fermionic systems in the electrical conductivity. This is an interesting regime because the relaxation of excitations appears to be larger than the excitation energy of the excitations themselves, indicating a breakdown of the Boltzmann approach. More recently, this concept has been extended to thermal transport properties of insulators where it is suggested that a similar lower bound appears in the thermal diffusivity D_th that is also characterized by the Planckian time D_th≥D_H=v_s²τ_H.

Here we propose a purely classical scenario where this thermal diffusion bound can be broken. Our model consists of highly non-linear unit cells connected by springs whose transport properties can be described by the phonon Green's function in the context of fluctuation-dissipation theorem. In this case, the thermal conductivity is mostly contributed by the sound mode while the other degrees of freedom remain incoherent. We will demonstrate this idea through an explicit example that can be computed nearly exactly. We expect our classical model to provide insight into the quantum limit through semiclassical approximations.