Thermal transport through a mesoscopic weak link - art. no. 155320

We calculate the rate of thermal energy flow between two macroscopic bodies , each in thermodynamic equilibrium at a different temperature, and joined by a weak mechanical link. The macroscopic solids are assumed to be electri cally insulating, so that thermal energy is carried only by phonons. To lea ding order in the strength of the weak link, modeled here by a harmonic spr ing, the thermal current is determined by a product of the local vibrationa l density-of-states of the two bodies at the points of connection. Our gene ral expression for the thermal current can be regarded as a thermal analog of the well-known formula for the electrical current through a tunneling ba rrier. It is also equivalent to the thermal Landauer formula in the weak-tu nneling limit. Implications for heat transport experiments on dielectric qu antum point contacts are discussed.