Comparison between two models of dephasing in mesoscopic systems

Two phenomenological models have been proposed in mesoscopic systems to study the role of inelastic scattering on the phase coherent motion of electrons. In the first one, due to Buttiker, one adds a voltage probe into the system (or in the scattering matrix). The second model invokes the complex (or optical) potential in the system Hamiltonian. Studying a simple geometry of a metallic loop in the presence of Aharonov-Bohm magnetic flux, we show that the two probe conductance is symmetric in the reversal of the magnetic field in Buttiker's approach. Whereas the two probe conductance within the complex potential model is asymmetric in the magnetic flux reversal contrary to the expected behavior. [S0163-1829(98)00115-5].