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Statistics of Current Fluctuations and Electron-Electron Interactions in Mesoscopic Coherent Conductors

Abstract

We formulate a general path integral approach which describes statistics of current fluctuations in mesoscopic coherent conductors at arbitrary frequencies and in the presence of interactions. Applying this approach to the non-interacting case, we analyze the frequency dispersion of the third cumulant of the current operator S3{\cal S}_3 at frequencies well below both the inverse charge relaxation time and the inverse electron dwell time. This dispersion turns out to be important in the frequency range comparable to applied voltages. For comparatively transparent conductors it may lead to the sign change of S3{\cal S}_3. We also analyze the behavior of the second cumulant of the current operator S2{\cal S}_2 (current noise) in the presence of electron-electron interactions. In a wide range of parameters we obtain explicit universal dependencies of S2{\cal S}_2 on temperature, voltage and frequency. We demonstrate that Coulomb interaction decreases the Nyquist noise. In this case the interaction correction to the noise spectrum is governed by the combination βˆ‘nTn(Tnβˆ’1)\sum_nT_n(T_n-1), where TnT_n is the transmission of the nn-th conducting mode. The effect of electron-electron interactions on the shot noise is more complicated. At sufficiently large voltages we recover two different interaction corrections entering with opposite signs. The net result is proportional to βˆ‘nTn(Tnβˆ’1)(1βˆ’2Tn)\sum_nT_n(T_n-1)(1-2T_n), i.e. Coulomb interaction decreases the shot noise at low transmissions and increases it at high transmissions.Comment: 12 pages, 3 figures. To be published in the Proceedings of the SPIE Symposium on Fluctuations and Noise, Maspalomas, Grand Canaria, Spain (May 2004

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