Quantum transport of electrons through a molecule is a series of individual electron tunneling events separated by stochastic waiting time intervals. We study the emergence of temporal correlations between successive waiting times for the electron transport in a vibrating molecular junction. Using the master equation approach, we compute the joint probability distribution for waiting times of two successive tunneling events. We show that the probability distribution is completely reset after each tunneling event if molecular vibrations are thermally equilibrated. If we treat vibrational dynamics exactly without imposing the equilibration constraint, the statistics of electron tunneling events become non-renewal. Non-renewal statistics between two waiting times ${\tau }_1$ and ${\tau }_2$ means that the density matrix of the molecule is not fully renewed after time ${\tau }_1$ and the probability of observing waiting time ${\tau }_2$ for the second electron transfer depends on the previous electron waiting time ${\tau }_1$. The strong electron-vibration coupling is required for the emergence of the non-renewal statistics. We show that in the Franck-Condon blockade regime, extremely rare tunneling events become positively correlated.

中文翻译：

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具有电子振动相互作用的分子结中电子传输的非更新统计

电子通过分子的量子传输是由随机等待时间间隔分隔开的一系列单个电子隧穿事件。我们研究了在振动分子结中电子传输的连续等待时间之间的时间相关性的出现。使用主方程方法，我们计算了两个连续隧穿事件的等待时间的联合概率分布。我们表明，如果分子振动达到热平衡，则在每次隧穿事件之后，概率分布将完全重置。如果我们在不施加平衡约束的情况下精确地处理振动动力学，则电子隧穿事件的统计信息将不会更新。两个等待时间之间的非更新统计${\tau }_{\mathrm{1个}}$ 和 ${\tau }_{\mathrm{2个}}$ 表示一段时间后分子的密度矩阵未完全更新 ${\tau }_{\mathrm{1个}}$ 观察等待时间的可能性 ${\tau }_{\mathrm{2个}}$ 第二次电子转移取决于先前的电子等待时间 ${\tau }_{\mathrm{1个}}$。非更新统计数据的出现需要强大的电子振动耦合。我们表明，在弗兰克-康东封锁制度中，极为罕见的隧道事件正相关。