Dynamical Properties of Quantum Hall Edge States

Abstract

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 $|<i|f>|\sim L^{-\frac{1}{2\nu }(\frac{\delta }{\pi }{)}^2}$ 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 one dimensional Fermi liquid into a QH fluid. It is argued that 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 $I\sim V^{1/\nu }$.

12 pages. Algebraic error in the tunneling exponent calculation in the last part of the paper is corrected. The orthogonality catastrophe and x-ray calculations are not affected by this error

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