Thermal susceptibility -- the nonlocal temperature response to local heat input

When a finite sample of a solid absorbs heat from an external source, the temperature response is interesting, especially in nanomaterials. Its understanding is important for heat management of circuit elements. Thermal susceptibility Θ(x-x’,t-t’) was defined by Allen and Perebeinos (2018) as the temperature rise at (x,t) per unit heat insertion at (x’,t’). This linear response function will be discussed for insulating crystals, where heat and temperature are described by phonons. For nanoscale studies, thermal susceptibility is a more useful and appropriate idea than thermal conductivity. It provides a more direct and visualizable understanding of the “ballistic to diffusive crossover”. Two particular issues will be discussed: (1) How can thermal susceptibility of nanoscale systems be studied by Boltzmann theory? (2) Are the results of Boltzmann theory reliable and useful for such systems? Can they help to interpret experiments and molecular dynamics simulations? A phonon Boltzmann theory appropriate for thermal susceptibility was given by Hua and Minnich (2014). The phonon distribution function N(Q) is driven not only by the usual terms, but also by external insertion of heat. This poses several interesting difficulties, which will be discussed. Numerical solutions are difficult unless the relaxation-time approximation is made. Computations will be discussed. These are being done in collaboration with Ali Kefayati and Vasili Perebeinos from University at Buffalo.