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Thermal transport through ac-driven transparent Josephson weak links

We discuss how phase coherence manifests in the heat transport through superconducting single and multichannel Josephson junctions in time dependent situations. We consider the heat current driven through the junction by a temperature difference in dc voltage and ac phase biased situations. At low bias, the electromagnetic driving mainly modifies the form of the coherent resonance that transports a large part of the heat current, rather than simply dissipating energy in the junction. We find a description for the heat current in terms of quasiparticle n-photon absorption and emission rates, and discuss analytical and numerical results concerning them. In addition to the ensemble average heat transport, we describe also its fluctuations.