Comparison between the two models of dephasing in mesoscopic systems

TL;DR

This paper compares two phenomenological models of dephasing in mesoscopic systems, revealing differences in their symmetry properties under magnetic flux reversal, which impacts understanding of inelastic scattering effects.

Contribution

It provides a detailed comparison of B"uttiker's voltage probe model and the complex potential model in mesoscopic systems, highlighting their differing symmetry behaviors.

Findings

B"uttiker's model shows symmetric conductance under magnetic flux reversal.

Complex potential model exhibits asymmetric conductance under flux reversal.

The results suggest limitations of the complex potential approach in capturing expected symmetries.

Abstract

In mesoscopic systems to study the role of inelastic scattering on the phase coherent motion of electrons two phenomenological models have been proposed. In the first one, due to B\"uttiker, 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 B\"uttiker's approach. Whereas the two probe conductance within the complex potential model is asymmetric in the magnetic flux reversal contrary to the expected behavior.