Oscillations of photonic heat current through parallel-coupled double circular mesoscopic Josephson junction devices

The parallel-coupled double circular mesoscopic Josephson junction devices connecting to two photon reservoirs are investigated, and the time-dependent photonic heat current formula is derived. The time-oscillating structures of heat current are contributed by the superposition of heat current branches with frequencies $$0,\pm \omega _i,\pm 2\omega _i$$ 0 , ± ω i , ± 2 ω i ( $$i=1,2$$ i = 1 , 2 ). The frequency ratio $$\omega _{2}/\omega _{1}$$ ω 2 / ω 1 of field-induced oscillation branches dominates the current evolution structure. The main oscillation wave package can be superposed by multiple resonant peaks as the two frequencies do not match entirely. As magnetic fluxes $$\Phi _{i}$$ Φ i possess the relation $$\Phi _{2}=m\Phi _{1}$$ Φ 2 = m Φ 1 , the dc photonic heat current versus $$\Phi _{1}$$ Φ 1 exhibits maximum values with equal height located at $$\Phi _{1}=n\Phi _{0}$$ Φ 1 = n Φ 0 , where m, n are integers, and $$\Phi _0$$ Φ 0 is the flux quantum. The main peaks are split to form multi-peak structure, and the number of split resonant peaks in a period $$\Phi _0$$ Φ 0 is equal to m. The detailed behavior is intimately ascribed to whether m being odd or even. Graphic abstract