Electronic heat current fluctuations in a quantum dot

The fluctuations of the heat current in a quantum dot coupled to electron reservoirs are calculated at finite frequency, voltage, and temperature using the nonequilibrium Green function technique. The nonsymmetrized heat noise is expressed as an integral on energy containing four contributions, each of which includes transmission amplitudes, electron-hole pair distribution functions, and energy difference factors. The effect of the asymmetry of the couplings between the quantum dot and the reservoirs is studied. Features of the heat noise are highlighted and discussed for an equilibrium and an out-of-equilibrium quantum dot. In the latter case and within the high transmission limit, the heat noise is closely related to the radiative power spectrum, leading to an out-of-equilibrium Planck's law. Proposals for the measurement of the heat noise are discussed.