Statistics of Charge Transport and Modified Time Ordering
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The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large detector and of a linear dispersion relation. The measurement of charge takes place according to various protocols. It is found that, as a rule, the statistics is expressed by means of time-ordered current correlators. However the ordering prescription differs from the usual ones (Dyson and Keldysh) by the Matthews modification. Nevertheless binomial statistics is confirmed in all cases.
KeywordsTime ordering Correlation functions Counting statistics Contact terms Transport theory
We thank S. Bachmann and M. Reznikov for valuable discussions and encouragement. The research of G.B. Lesovik was supported by the Russian Foundation for Basic Research (grant No. 11-02-00744-a); that of A.V. Lebedev by the Swiss National Science Foundation through the National Center of Competence in Research on Quantum Science and Technology (QSIT). Collaboration was made possible by the Pauli Center. All supports are gratefully acknowledged.
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