Nonlocal thermal transport modeling using thermal susceptibility

If heat current in crystals is probed on length scales smaller than phonon mean free paths, the current j at point r is not a local function of the local temperature, T(r), or its gradient, grad T(r). Ballistic heat transport depends on non-locally on thermal behavior at other points, r’. Thermal susceptibility, Θ(r,r’), is the temperature response of the system at point r to the heat input at point r’. The non-local effects have to be considered rigorously for an accurate interpretation of experimental measurements and theoretical investigations. Here, we investigate the ability of the thermal susceptibility in taking into account the non-local effects by using Boltzmann theory. Our results illustrate that thermal transport modeling using the thermal susceptibility function accurately reveals the nonlocal effects from ballistic to diffusive transport regimes.