Coastal Kelvin Mode and the Fractional Quantum Hall Edge

This letter explores the relationship between the coastal Kelvin mode observed in the shallow water model of ocean waves and the edge mode of a fractional quantum Hall (FQH) state. The hydrodynamic equations for the FQH state can be written as a generalized form of the shallow water equations with Coriolis force, where the density replaces the height of the fluid column and the magnetic field plays the role of the Coriolis parameter. In the FQH case, the potential vorticity associated with the shallow water model becomes a constant. In contrast to the shallow water equations, the hydro system for the FQH state contains higher derivatives of velocity which enforces the no-stress boundary condition in addition to the no-penetration condition at the hard wall or coastal boundary. For these boundary conditions, the linearized edge dynamics has two chiral edge modes propagating in the same direction: a non-dispersing Kelvin mode and a dispersing chiral boson mode. We investigate the nature of these modes in the presence of a tangent electric field. Our results show that the Kelvin mode cannot be excited by this field, and as a result, it cannot transport charge along the edge. However, the dispersive chiral boson mode is compatible with the edge dynamics of the FQH state and satisfies the anomaly equation.