用纠缠态表象发展介观电路量子理论

The present application is aimed at generating a systematic quantization theory of mesoscopic circuit stemming from the conventional electric circuit theory, which is based on quantum entanglement theory. By indicating that quantum entanglement is the intrinsic property of two or more coupled electric loops, we propose to analyze and solve various coupled mesoscopic circuits, by using the quantum mechanical entangled state representation constructed by ourselves, not only find the eigenstate (which is a squeezed state, but also an entangled state), but also gives its characteristic frequency equivalent to a single LC loop, which remains for experimental verification. We shall also explore the new physical quantities that cannot be derived in the context of the Kirchhoff's law, so ours work will be a breakthrough for the traditional Kirchhoff 's electric voltage and current formalism. Dissipation and diffusion effect of the mesoscopic circuit in external electromagnetic field are also studied by solving some quantum master equations with use of the entangled state representation. Our study will highlight the ubiquitous quantum entanglement in the quantum mesoscopic circuit and its corresponding effective processing method, which will open up a new research area and content beyond the traditional electrical and electronic engineering as well as promote the development of theory of quantum mechanics.

本申请旨在从传统的电路理论发展出一套立足于量子纠缠的介观电路量子化理论。在指出量子纠缠是两个以上耦合回路的内禀性质的基础上，提出用申请人构建的量子力学纠缠态表象来分析和求解有各种耦合的介观电路，不但找到其哈密顿量的本征态（是压缩态，也是量子纠缠态）的具体形式，而且给出其特征频率，以便于实验验证。同时还将探索用基尔霍夫定律无法导出的新物理量，这是对传统的用基尔霍夫电压电流定律分析电路的一个突破。对于介观电路的耗散、外电磁场对它的扩散效应等，也通过用纠缠态表象解若干量子主方程的方案来处理。以上研究将凸显量子化介观电路中无处不在的量子纠缠及相应的有效处理方法，为传统的电工电子学提供新的研究方向和新的内容，同时也推动量子力学理论的发展。

本项目从传统的电路理论发展出了一套立足于量子纠缠的介观电路量子化理论；在量子力学的框架内求解了各种形式的耦合介观电路，不但找到其哈密顿量的本征态的具体形式，而且给出其特征频率，取得了一系列的创新成果。同时还求解出用基尔霍夫定律无法导出的新物理量，这是对传统的用基尔霍夫电压电流定律分析电路的一个突破。此外，也研究了介观电路的耗散、外电磁场对它的扩散效应等，通过用纠缠态表象解出了若干介观电路的量子主方程。我们的研究将凸显量子化介观电路中无处不在的量子纠缠及相应的有效处理方法，为传统的电工电子学提供新的研究方向和新的内容，同时也推动量子力学理论的发展。项目执行期间共发表文章30篇，专著2本，培养博士生1名，超额完成预定目标。