DYNAMICAL PROPERTIES OF QUANTUM HALL EDGE STATES

We consider the dynamical properties of simple edge states in integer (nu=1) and fractional (nu=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]\similar to L(-(1/2 nu)(delta/pi)2) with the phase shift delta. The transition probability for the x-ray problem is also found with the index, dependent on nu. 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 similar to V-1/nu.