The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.

中文翻译：

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量子动力学中朗道运输的出现：一种模型哈密顿方法

用于计算纳米级设备中电流-电压特性的Landauer表达式有效，但不适用于瞬态现象和随时间变化的电流，因为它仅在外部扰动后电荷载流子转变为稳定通量时才适用。在本文中，我们为电极-分子-电极排列中的时间相关电流构建了一个非常通用的表达式。利用模型哈密顿量（由子系统能级及其电子耦合项组成），我们传播薛定er波函数方程，以数值方式计算各个子系统中随时间变化的总体。每个电极中的电流（根据相应的总体变化率定义）具有两个分量，一种是由于电荷源自同一电极，另一种是由于电荷最初位于另一电极。我们导出了第一个分量的解析表达式，并说明它在早期就与其数值对应物合理地吻合。利用波函数的单位演化，我们构建了一个更通用的Landauer样式公式，并从我们的仿真中说明了Landauer传输的出现，而没有假设时间独立的电荷流。我们的广义Landauer公式在任何时候都适用于超出宽带限制的模型，状态的电极密度不均匀以及子系统之间时间和能量相关的电子耦合。随后，我们研究了模型中调节该稳态起始时间尺度的成分。我们将一般电流表达式的性能与Landauer电流进行比较，以进行时变电子耦合。最后，我们评论了Landauer公式在计算等离激元去相干引起的热电子电流时的适用性。