  Inelastic scattering induces dephasing in mesoscopic systems. An analysis of
previous models to simulate inelastic scattering in such systems is presented
and also a relatively new model based on wave attenuation is introduced. The
problem of Aharonov-Bohm(AB) oscillations in conductance of a mesoscopic ring
is studied. We have shown that conductance is symmetric under flux reversal and
visibility of AB oscillations decay to zero as function of the incoherence
parameter, signalling dephasing. Further wave attenuation is applied to a
fundamental problem in quantum mechanics, i.e., the
conditional(reflection/transmission) times spent in a given region of space by
a quantum particle before scattering off from that region.
