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

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 ${\cal S}_3$ 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 ${\cal S}_3$. We also analyze the behavior of the second cumulant of the current operator ${\cal S}_2$ (current noise) in the presence of electron-electron interactions. In a wide range of parameters we obtain explicit universal dependencies of ${\cal S}_2$ 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 $\sum_nT_n(T_n-1)$, where $T_n$ is the transmission of the $n$-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 $\sum_nT_n(T_n-1)(1-2T_n)$, 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

Strong Electron Tunneling through a Small Metallic Grain

Electron tunneling through mesoscopic metallic grains can be treated perturbatively only provided the tunnel junction conductances are sufficiently small. If it is not the case, fluctuations of the grain charge become strong. As a result (i) contributions of all -- including high energy -- charge states become important and (ii) excited charge states become broadened and essentially overlap. At the same time the grain charge remains discrete and the system conductance $e$-periodically depends on the gate charge. We develop a nonperturbative approach which accounts for all these features and calculate the temperature dependent conductance of the system in the strong tunneling regime at different values of the gate charge.Comment: revtex, 8 pages, 2 .ps figure

ПРОБЛЕМИ ДУХОВНО-МОРАЛЬНОГО ВИХОВАННЯ МОЛОДІ НА ЗАСАДАХ ХРИСТИЯНСЬКОГО ВІРОВЧЕННЯ У ЗАСОБАХ МАСОВОЇ ІНФОРМАЦІЇ РІВНЕНЩИНИ. (Problems of spiritual and moral education of young people on the principles of the Christian Doctrine in the mass media of the Rivne region.)

У статті розкрито тему важливості духовно-морального виховання молоді на засадах християнського віровчення через засоби масової інформації; проаналізовано сучасний стан його здійснення в інформаційному просторі Рівненщини та подано рекомендації щодо напрямків роботи з метою поліпшення існуючої ситуації у даній сфері. (In this article we discuss the importance of educating young people on spiritual and moral principles which are based on teaching of Christianity and how it is represented in the mass media; we analyze its current situation in informational space of Rivne region and give the recommendations how to improve today's situation in this sphere.

New Examples of Systems of the Kowalevski Type

A new examples of integrable dynamical systems are constructed. An integration procedure leading to genus two theta-functions is presented. It is based on a recent notion of discriminantly separable polynomials. They have appeared in a recent reconsideration of the celebrated Kowalevski top, and their role here is analogue to the situation with the classical Kowalevski integration procedure.Comment: 17 page