  In this letter, we investigate the dissipative dynamics at the edge of
Laughlin fractional quantum Hall (FQH) states starting from the hydrodynamic
framework of the composite Boson theory recently developed in arXiv:2203.06516.
Critical to this description is the choice of boundary conditions, which
ultimately stems from the choice of hydrodynamic variables in terms of
condensate degrees of freedom. Given the gapped nature of bulk, one would
expect dissipation effects to play an important role only near the FQH edge.
Thus, one envisions a scenario where the bulk hydro equations remain
unmodified, while the dissipation effects are introduced at the edge via
boundary conditions. We have recently shown that the anomaly requirements fix
the boundary conditions of the FQH fluid to be no-penetration and no-stress
boundary conditions. In this work, we introduce energy dissipation in the
no-stress boundary condition leading to charge diffusion at the boundary. The
resulting dissipative edge dynamics is quite rigid from a hydro perspective, as
it has to preserve the edge charge continuity and the anomaly structure. We
show that the diffusive edge dynamics with fluctuation-dissipation relations
within a power counting scheme belong to the Kardar-Parisi-Zhang universality
class.
