Noises in a two-channel charge Kondo model

We investigate fluctuations of electric and heat currents, along with their cross-correlations, in a two-channel charge Kondo circuit driven by either a voltage bias or a temperature gradient applied across the weak link. The ratios of voltage-driven electric/heat noise to the applied voltage $V$ exhibit oscillations with the gate voltage $N$, resembling the behavior of the thermoelectric coefficient $G_T$. In contrast, the ratios of temperature-driven electric/heat noise to the temperature difference $\Delta T$ vary with $N$ in a manner analogous to the thermal coefficient $G_H$ or the electric conductance $G$. The mixed noise, which is defined as the correlation function between electric and heat currents, displays behavior opposite to that of the above noises. The logarithmic temperature dependence of these noises signals non-Fermi-liquid behavior, while their oscillations with gate voltage reflect the roles of particle-hole and time-reversal symmetries in thermoelectric transport. Our results demonstrate that the fundamental relations linking voltage- and temperature-induced noises to thermoelectric transport across a tunnel junction persist beyond the Fermi-liquid paradigm.