Dissipative edge dynamics of FQH fluids

Recently it was shown that the Laughlin states of the fractional quantum hall effect, on a domain with boundaries, can be mapped to a hydrodynamic system with no-penetration and no-tangent stress boundary conditions, along with an additional constraint known as the Hall constraint [1]. The no-stress condition is derived from conservation of energy, and gives rise to conservation of charge at the boundary. In this work, we relax conservation of energy to allow for dissipation in the boundary, while retaining the gapped bulk dynamics. This modifies the no-stress condition and changes the edge current, leading to diffusive charge transport in the boundary. We present the formalism for edge dissipation in the context of fluid dynamics, and examine the linearized system. We also discuss possible extensions to a nonlinear analysis.

[1] G. M. Monteiro, V. Nair, and S. Ganeshan. Topological fluids and FQH edge dynamics. arXiv preprint arXiv:2203.06516 (2022).