Some analytical results for the steady-state properties of the single-molecule tunneling junction are obtained with the use of the broadened classical master equations and classical master equations. The case of the one electronic level of the bridge molecule coupled to a single classical harmonic oscillator is considered within the spin-less model. Based on these equations, we establish some relations between different average values of interest, considering the large bias limit and the limit of the weak electron–oscillator coupling. We derive the analytical expressions for a number of characteristic properties of the tunneling junction in these limiting cases, compare our results with those obtained by the numerically exact calculations, and find that our expressions work very well. In the diabatic regime, the approximate solutions of the classical master equations are suggested, which permit us to introduce the effective temperature T_eff and perform rather simple calculations of the average vibrational excitations N and the tunnel current I. It is shown that in the adiabatic regime, the properties of the tunneling junction depend essentially on the effective temperature T_{eff ad}. We obtain the analytical expressions for T_{eff ad} using different approaches for the treatment of the adiabatic regime. For both the diabatic and adiabatic regimes, we calculate T_eff, T_{eff ad}, N, and I, compare our results with those available in the literature, and confirm well agreement. The dependence of N and I on the reorganization energy and the position of the electronic level of the bridge molecule is discussed.

中文翻译：

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经典主方程和扩展的经典主方程：一些分析结果

使用扩展的经典主方程和经典主方程获得了单分子隧道结稳态特性的一些分析结果。在无自旋模型中考虑了桥分子的一个电子能级耦合到单个经典谐振子的情况。基于这些方程，我们在不同的感兴趣平均值之间建立了一些关系，考虑到大偏置限制和弱电子振荡器耦合的限制。我们推导出了这些极限情况下隧道结的许多特征属性的解析表达式，将我们的结果与通过数值精确计算获得的结果进行比较，发现我们的表达式工作得很好。在绝热状态下，T _eff并执行相当简单的平均振动激励N和隧道电流I 计算。结果表明，在绝热状态下，隧道结的特性主要取决于有效温度T _{eff ad}。我们使用不同的方法处理绝热状态，获得了T _{eff ad}的解析表达式。对于非绝热和绝热状态，我们计算T _eff、T _{eff ad}、N和I，将我们的结果与文献中的结果进行比较，并确认一致。的依赖讨论了N和I对桥分子的重组能和电子能级位置的影响。