Non-linear edge dynamics of an integer quantum Hall fluid(a)(a)Contribution to the Focus Issue Turbulent Regimes in Bose-Einstein Condensates edited by Alessandra Lanotte, Iacopo Carusotto and Alberto Bramati.

Abstract

We report a theoretical study of the linear and nonlinear dynamics of edge excitations of an integer quantum Hall state of non-interacting fermions. New features beyond the chiral Luttinger liquid picture are anticipated to arise from the interplay of the curvature of the Landau level dispersion and of the Pauli exclusion principle. For long-wavelength perturbations, the microscopic numerical results are captured by a chiral nonlinear hydrodynamic equation including a density-dependent velocity term. In the wave-breaking regime, shock waves are found to be regularized into a complex ripple pattern by higher-order dispersive effects. Our results are of specific relevance for experiments with synthetic quantum matter, in particular ultracold atomic gases.