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Static and dynamical transport properties of the fractional quantum Hall (FQH) states are studied based on the theory of the edge excitations. Because the electrons on the edge of the FQH states are strongly correlated, the I-V curve is, in general, nonlinear and contains singular structures. A narrow-band noise is found in the dc transport of the FQH states, which can be used to directly measure the fractional charge of the quasiparticles. The long-range Coulomb interaction is also discussed, which is found to have a profound effect on the transport properties of the integer quantum Hall and FQH states. In particular, the long-range interaction will cause a breakdown of the quantized conductance in narrow quantum Hall samples. As a closely related problem, we also study the transport properties of a one-dimensional charge-density-wave state in the presence of a single weak impurity. An exact mapping between two-dimensional quantum Hall systems and one-dimensional electron models is found.
Xiao-Gang Wen (Sun,) studied this question.