  Decoherence is an undesirable, but ubiquitous phenomenon in quantum systems.
Here, we study the effect of partial decoherence, induced via a B\"uttiker
probe, on two-terminal electronic transport across one-dimensional quantum
wires and rings, in both the linear and non-linear regimes. We find that
dephasing causes backscattering when introduced locally in a ballistic channel.
Further, we find that decoherence results in rectification when inversion is
broken in the two-terminal transport set-up by a combination of a local
dephasing centre and a static impurity. Interestingly, the rectification
strength and even its direction varies strongly with the relative distance
between the probe and the scatterer. We further analyze how decoherence affects
characteristic quantum effects in electronic transport, such as, Fabry-P\'erot
oscillations in double-barrier setups, and Aharonov-Bohm interference in
one-dimensional rings, and find that the amplitude of oscillations in
conductance is reduced by decoherence.
