**7. Conclusions**

In this work, we investigated charge-heat mixed noise and heat noise generated by a periodic time-dependent voltage in a quantum point contact geometry implemented in a quantum Hall bar. We focused on the weak backscattering regime of the tunneling barrier and we evaluated fluctuations of charge and heat currents at lowest order in tunneling the amplitude. We provided a spectroscopic analysis of these quantities by tuning independently the AC and DC amplitudes of the voltage drive for integer and fractional filling factors. By focusing on a cosine drive and a periodic train of Lorentzian pulse, we proved that both charge-heat noise and heat noise reveal the symmetry properties of the photo-assisted coefficients of the applied drive. The different power-laws that govern the behavior of mixed and heat noises give rise to two distinct profiles when these quantities are plotted as a function of the AC amplitude. In particular, charge-heat noise displays an opposite monotonicity for the case of integer and fractional filling factors, thus revealing the presence of a sub-linear power-law decay typical of Luttinger liquid physics.

**Author Contributions:** Conceptualization, F.R., M.A. and D.F.; formal analysis, M.A. and D.F.; writing—original draft preparation, F.R., M.A. and D.F.; writing—review and editing, J.R., T.J., T.M. and M.S.; supervision, T.M. and M.S.

**Funding:** This work was granted access to the HPC resources of Aix-Marseille Université financed by the project Equip@Meso (Grant No. ANR-10-EQPX29-01). It has been carried out in the framework of project "one shot reloaded" (Grant No. ANR-14-CE32-0017) and benefited from the support of the Labex ARCHIMEDE (Grant No. ANR11-LABX-0033) and the AMIDEX project (Grant No. ANR-11-IDEX-0001-02), funded by the "investissements d'avenir" French Government program managed by the French National Research Agency (ANR).

**Acknowledgments:** The authors thank Luca Vannucci for useful discussions.

**Conflicts of Interest:** The authors declare no conflict of interest.
