We formulate a general path integral approach which describes statistics ofcurrent fluctuations in mesoscopic coherent conductors at arbitrary frequenciesand in the presence of interactions. Applying this approach to thenon-interacting case, we analyze the frequency dispersion of the third cumulantof the current operator ${\cal S}_3$ at frequencies well below both the inversecharge relaxation time and the inverse electron dwell time. This dispersionturns out to be important in the frequency range comparable to appliedvoltages. For comparatively transparent conductors it may lead to the signchange of ${\cal S}_3$. We also analyze the behavior of the second cumulant ofthe current operator ${\cal S}_2$ (current noise) in the presence ofelectron-electron interactions. In a wide range of parameters we obtainexplicit universal dependencies of ${\cal S}_2$ on temperature, voltage andfrequency. We demonstrate that Coulomb interaction decreases the Nyquist noise.In this case the interaction correction to the noise spectrum is governed bythe 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 theshot noise is more complicated. At sufficiently large voltages we recover twodifferent interaction corrections entering with opposite signs. The net resultis proportional to $\sum_nT_n(T_n-1)(1-2T_n)$, i.e. Coulomb interactiondecreases the shot noise at low transmissions and increases it at hightransmissions.
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机译：我们制定了一种一般路径积分方法，该方法描述了介观相干导体在任意频率和存在相互作用的情况下电流波动的统计数据。将这种方法应用于非相互作用情况，我们分析了电流算子$ {\ cal S} _3 $的第三累积量在远低于反电荷弛豫时间和反电子停留时间的频率下的频散。事实证明，在与施加电压相当的频率范围内，该色散很重要。对于相对透明的导体，可能导致$ {\ cal S} _3 $的符号变化。我们还分析了在存在电子-电子相互作用的情况下，当前算子$ {\ cal S} _2 $（电流噪声）的第二累积量的行为。在各种各样的参数中，我们获得了$ {\ cal S} _2 $对温度，电压和频率的明确通用依存关系。我们证明了库仑相互作用降低了奈奎斯特噪声，在这种情况下，对噪声谱的相互作用校正由组合$ \ sum_nT_n（T_n-1）$控制，其中$ T_n $是第n次传导模式的传输。电子-电子相互作用对散粒噪声的影响更为复杂。在足够大的电压下，我们恢复两个不同的相互作用校正，并以相反的符号输入。净结果与$ \ sum_nT_n（T_n-1）（1-2T_n）$成正比，即库仑相互作用会降低低传输时的散粒噪声，而在高传输时会增加散粒噪声。
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