  The influence of Rashba spin-orbit coupling on zero conductance resonances
appearing in one dimensional ring asymmetrically coupled to two leads is
investigated. For this purpose, the transmission function of the corresponding
one-electron scattering problem is derived analytically and analyzed in the
complex energy plane with focus on the zero-pole structure characteristic of
transmission (anti)resonances. The lifting of real conductance zeros due to
spin-orbit coupling in the asymmetric Aharonov-Casher (AC) ring is related to
the breaking of spin reversal symmetry in analogy to the time-reversal symmetry
breaking in the asymmetric Aharonov-Bohm (AB) ring.
