High-order counting statistics and interactions

Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures [1]. Recently it has been shown that the charge transport statistics for noninteracting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events, and the zeros of the generating function are real and negative [2]. In this talk I show how the zeros of the generating function move into the complex plane due to interactions and demonstrate how the positions of the zeros can be detected using high-order factorial cumulants [3]. As an illustrative example I discuss electron transport through a Coulomb blockade quantum dot for which the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. These findings are important for understanding the influence of interactions on counting statistics, and the characterization in terms of zeros of the generating function provides a simple interpretation of recent experiments, where high-order statistics have been measured [4]. \\[4pt] [1] Yu. V. Nazarov, ed., Quantum Noise in Mesoscopic Physics, NATO Science Series, Vol. 97 (Kluwer, Dordrecht, 2003) \newline [2] A. G. Abanov and D. A. Ivanov, Phys. Rev. Lett. 100, 086602 (2008), Phys. Rev. B 79, 205315 (2009) \newline [3] D. Kambly, C. Flindt, and M. B\"{u}ttiker, Phys. Rev. B 83, 075432 (2011) -- Editors' Suggestion \newline [4] C. Flindt, C. Fricke, F. Hohls, T. Novotn\'{y}, K. Netocn\'{y}, T. Brandes, and R. J. Haug, Proc. Natl. Acad. Sci. USA 106, 10116 (2009)