Vacuum-induced phonon transfer between two solid dielectric materials: Illustrating the case of Casimir force coupling

The natural transition from the radiative regime to the conductive regime of heat transfer between two identical isotropic nonmagnetic dielectric solid materials is questioned by investigating the possibility of induced phonon transfer in vacuum. We describe the process in a general way assuming a certain phonon coupling mechanism between the two identical solids, then we particularly illustrate the case of coupling through the Casimir force. We analyze how this mechanism of heat transfer compares and competes with the near field thermal radiation using a local model of the dielectric function. We show that the former mechanism can be very effective and even surpass the latter mechanism depending on the nature of the solid dielectric materials, the distance gap between them, as well as the operating temperature regime.