Equilibration to the steady state for a wide class of Luttinger liquid ballistic weakly linked tunnel contacts is extensively studied. Quantum fluctuations of tunnel current are considered in all orders in tunnel coupling and out of the equilibrium in the time domain. Especially, two important mathematical statements: Self-equilibration (SE-)theorem and Self-equilibration (SE-)lemma on the exact re-exponentiation of thermal average from the Keldysh-contour-ordered evolution operator for arbitrary weakly linked Luttinger liquid tunnel contact are proven. Demonstrated proof of SE-theorem and SE-lemma represents first evidence of a novel emergent phenomenon of "self-equilibration" in the dynamics of quantum fluctuations of electron transport through ballistic tunnel junctions. This phenomenon and all related real-time full counting statistics are shown to be much more general as compared to the usual Levitov-Lesovik scattering approach for the non-interacting electrons, though SE-theorem also contains known results obtained within the Levitov-Lesovik scattering approach as corresponding limiting case for lowest order cumulants at $ g=1 $. As the result, corresponding differential equation of "self-equilibration" for time-dependent Keldysh partition function of tunnel contact is derived and explained. As the consequence of obtained results, a universal character of self-equilibration of tunnel current in one-dimensional weakly linked tunnel junctions is revealed and studied on the level of non-equilibrium Fano factor. As well, a new measure of disequilibrium in such systems - the "steady flow" rate - is also introduced and discussed.

中文翻译：

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相互作用电子的量子点接触中的自平衡定理：超越 Levitov-Lesovik 散射方法的隧道传输的时间相关量子涨落

广泛研究了各种 Luttinger 液体弹道弱连接隧道接触的稳态平衡。隧道电流的量子涨落在隧道耦合和时域平衡之外的所有阶数中都被考虑。特别是，两个重要的数学陈述：自平衡 (SE-) 定理和自平衡 (SE-) 引理对任意弱链接 Luttinger 液体隧道接触的 Keldysh 轮廓有序演化算子的​​热平均值的精确重新取幂被证明。SE 定理和 SE 引理的证明证明了电子传输通过弹道隧道结的量子涨落动力学中“自平衡”的新出现现象的第一个证据。与用于非相互作用电子的常用 Levitov-Lesovik 散射方法相比，这种现象和所有相关的实时全计数统计数据显示出更普遍的情况，尽管 SE 定理也包含在 Levitov-Lesovik 散射中获得的已知结果方法作为最低阶累积量在 $ g=1 $ 时的相应极限情况。据此推导出并解释了隧道接触时效Keldysh配分函数的“自平衡”微分方程。作为所得结果的结果，在一维弱连接隧道结中隧道电流自平衡的普遍特征被揭示并在非平衡 Fano 因子的水平上进行研究。同样，这种系统中不平衡的一种新措施——“稳定流”