Voltage and dephasing probes: a full counting statistics discussion

TL;DR

This paper develops a full counting statistics framework to analyze voltage and dephasing probes in mesoscopic conductors, revealing their effects on transport and the conditions under which different models are equivalent.

Contribution

It introduces a detailed full counting statistics approach to compare voltage and dephasing probes, establishing conditions for their equivalence and analyzing phase distribution functions.

Findings

Single-channel probes are equivalent under a uniform phase distribution.

Chaotic cavities with long dwell times produce a uniform phase distribution.

Multi-channel or multiple probes show differences in transport statistics.

Abstract

Voltage and dephasing probes introduce incoherent inelastic and incoherent quasi-elastic scattering into a coherent mesoscopic conductor. We discuss in detail the concepts of voltage and dephasing probes and develop a full counting statistics approach to investigate their effect on the transport statistics. The formalism is applied to several experimentally relevant examples. A comparison of different probe models and with procedures like phase averaging over an appropriate phase distribution shows that there is a perfect equivalence between the models for the case of one single-channel probe. Interestingly, the appropriate phase distribution function is found to be uniform. A uniform distribution is provided by a chaotic cavity with a long dwell time. The dwell time of a chaotic cavity plays a role similar to the charge response time of a voltage or dephasing probe. For multi-channel or multiple probes the transport statistics of voltage and dephasing probes differs and the equivalence with phase averaging is similarly lost.