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The band structure of a quantum wire with the Rashba spin-orbit couplingdevelops a pseudogap in the presence of a magnetic field along the wire. Insuch a system spin mixing at the Fermi wavevectors $-k_F$ and $k_F$ can bedifferent. We have investigated theoretically the collective mode of thissystem, and found that the velocity of this collective excitation dependssensitively on the strength of the Rashba spin-orbit interaction and magneticfield. Our result suggests that the strength of the spin-orbit interaction canbe determined from the measurement of the velocity.Comment: RevTeX 4 file, 4pages, 6 eps figures. To appear in Physical Review

Collective excitation of quantum wires and effect of spin-orbit coupling in the presence of a magnetic field along the wire