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 a 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.