Heat flux in chiral and non-chiral quasi-one-dimensional systems with intrinsic dissipation

In this talk we explore a one-dimensional chiral system with an intrinsic mechanism of dissipation. Measurements of the energy relaxation in the integer quantum hall edge at filling factor \nu =2 show  the breakdown of heat current quantization [H. le Sueur et al., Phys. Rev. Lett. 105, 056803]. It was shown that dissipative neutral modes contributing less than a quantum of heat can be an explanation for the missing heat flux [A Goremykina et al., arXiv preprint arXiv:1908.01213]. In the previous analysis, using a hydrodynamic approach, it was necessary to introduce a UV cut-off given by the transverse size of the neutral modes. In this work we present an effective model of a dissipative quantum hall edge, which takes into account the full range of momenta. We mapped the QHE to a transmission line by analogy and used the Langevin method to extract the heat current in the presence of weak and strong dissipation. We proceed to generalize our results to non-chiral systems.