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We study the effect of spin-orbit interaction and in-plane effective magnetic field on the conductance of a quasi-one-dimensional ballistic electron system. The effective magnetic field includes the externally applied field, as well as the field due to polarized nuclear spins. The interplay of the spin-orbit interaction with effective magnetic field significantly modifies the band structure, producing additional subband extrema and energy gaps, introducing the dependence of the subband energies on the field direction. We generalize the Landauer formula at finite temperatures to incorporate these special features of the dispersion relation. The obtained formula describes the conductance of a ballistic conductor with an arbitrary dispersion relation.

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