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We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors acquire energy gap . At energies larger than , where is the impurity scattering rate, and for , where is the fluctuation velocity, the gap leads to an ``ideal’’ drag with almost equal currents in the conductors. At low energies the drag is suppressed by coherent instanton tunneling, and the zero-temperature transconductance vanishes, indicating the Fermi liquid behavior.

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