The purpose of this paper is to investigate the two-capacitor paradox using circuit models developed in the analysis of circuits that include nanoelectronic single-electron tunneling devices. The two-capacitor paradox, in which it seems that energy is not conserved in a simple circuit consisting of two capacitors in parallel separated by an ideal switch, is resolved by applying linear circuit theory utilizing a current-described by a (Dirac) delta function-and stepping voltages across all three elements. Based on a similar description, successfully used for tunneling of electrons through metal junctions in nanoelectronics, the switch is modeled as a device across which-upon closing-the voltage steps down while the current through it is an impulse. The model distinguishes three intervals in describing the ideal switch: t <; 0, t = 0, and t > 0. As a consequence, the ideal switch dissipates energy during the switching action at t = 0 in zero time. Although the solution of the two-capacitor problem looks like a theoretical curiosity, the application of nanoelectronic concepts allow a physical explanation based on electron tunneling; it shows that the ideal switch is best described by the tunneling of many electrons. In such a context, some of those electrons loose energy and the v-i characteristic shows Ohm's law.

中文翻译：

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通过与单电子电子学的相似性解决双电容器问题


本文的目的是使用在分析包括纳米电子单电子隧道器件的电路时开发的电路模型来研究双电容器悖论。双电容器悖论，即在由理想开关分隔的两个并联电容器组成的简单电路中，能量似乎不守恒，通过应用线性电路理论，利用由（狄拉克）δ 函数描述的电流，可以解决双电容器悖论。 -以及所有三个元件之间的步进电压。基于类似的描述，该开关成功地用于通过纳米电子学中的金属结隧道传输电子，该开关被建模为一种器件，在闭合时电压会下降，而通过它的电流是脉冲。该模型在描述理想开关时区分了三个区间：t <； 0、t = 0 和 t > 0。因此，理想开关在零时间 t = 0 的开关动作期间会消耗能量。尽管两个电容器问题的解决方案看起来像是理论上的好奇心，但纳米电子概念的应用允许基于电子隧道的物理解释；它表明，理想开关最好由许多电子的隧道效应来描述。在这种情况下，其中一些电子会失去能量，并且 vi 特性显示欧姆定律。