Dynamical properties of quantum Hall edge states.

We consider the dynamical properties of simple edge states in integer (ν = 1) and fractional (ν = 1/2m + 1) quantum Hall (QH) liquids. The influence of a time-dependent local perturbation on the ground state is investigated. It is shown that the orthogonality catastrophe occurs for the initial and final state overlap | < i|f > | ∼ L − 1 2ν (δ π) 2 with the phase shift δ. The transition probability for the x-ray problem is also found with the index, dependent on ν. Optical experiments that measure the x-ray response of the QH edge are discussed. We also consider electrons tunneling from one dimensional Fermi liquid into a QH fluid. For any filling fraction the tunneling from a Fermi liquid to the QH edge is suppressed at low temperatures and we find the nonlinear I − V characteristics I ∼ V 1/ν. The quantum Hall (QH) liquid is an incompressible state, where all bulk excitations have finite energy gaps. As for any incompressible liquid, droplet of water being the simplest example, the only low energy excitations are surface modes. Upon quantizing these surface modes one arrives at the picture of the simple propagating excitations on the surface of the droplet. For the two dimensional QH liquid these excitations represent the extended gapless 1