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We study the transport properties of a quantum wire, described by theTomonaga-Luttinger model, in the presence of a backscattering potentialprovided by several extended time-dependent impurities (barriers). Employingthe B\" uttiker-Landauer approach, we first consider the scattering ofnoninteracting electrons ($g=1$) by a rectangular-like barrier and find anexact solution for the backscattering current, as well as a perturbativesolution for a weak static potential with an arbitrary shape. We then includeelectron-electron interactions and use the Keldysh formalism combined with thebosonization technique to study oscillating extended barriers. We show that thebackscattering current off time-dependent impurities can be expressed in termsof the current for the corresponding static barrier. Then we determine thebackscattering current for a static extended potential, which, in the limit ofnoninteracting electrons ($g=1$), coincides with the result obtained using theB\" uttiker-Landauer formalism. In particular, we find that the conductance canbe increased beyond its quantized value in the whole range of repulsiveinteractions $0<g<1$ already in the case of a single oscillating extendedimpurity, in contrast %contrary to the case of a point-like impurity, wherethis phenomenon occurs only for $0<g<1/2$.Comment: 9 pages, 5 figure

Transport properties of a quantum wire: Role of extended time-dependent impurities