Two phenomenological models have been proposed in mesoscopic systems t
o study the role of inelastic scattering on the phase coherent motion
of electrons. In the first one, due to Buttiker, one adds a voltage pr
obe into the system (or in the scattering matrix). The second model in
vokes the complex (or optical) potential in the system Hamiltonian. St
udying a simple geometry of a metallic loop in the presence of Aharono
v-Bohm magnetic flux, we show that the two probe conductance is symmet
ric in the reversal of the magnetic field in Buttiker's approach. Wher
eas the two probe conductance within the complex potential model is as
ymmetric in the magnetic flux reversal contrary to the expected behavi
or. [S0163-1829(98)00115-5].