介观动力学中的可积性
Integrability in the mesoscopic dynamics
摘要：
介观力学（MeM），这已经介绍了在以前的文件，是有关的电子气限制在两个空间维度。它预言了关联电子对外部磁场的集体响应的一种特殊方式。该理论的动力学变量是一个有限维算子，它需要满足介观薛定谔方程（参见图1）。文本）。在这篇文章中，我们描述了介观薛定谔方程的一般解。我们的方法是针对手头的问题的。它依赖于方程的独特结构，除了酉群的几何之外，没有参考任何其他技术。最后，一个令人惊讶的事实浮出水面。也就是说，介观动力学通过（微观）薛定谔动力学“过滤”，因为后者是演化的一个明显可分离的部分，事实上是一个自主因素。从物理观点来看，这也是一个理想的结果。
英文摘要：
The Mesoscopic Mechanics (MeM), which has been introduced in a previous paper, is relevant to the electron gas confined to two spatial dimensions. It predicts a special way of collective response of correlated electrons to the external magnetic field. The dynamic variable of this theory is a finite-dimensional operator, which is required to satisfy the mesoscopic Schrödinger equation (cf. text). In this article, we describe general solutions of the mesoscopic Schrödinger equation. Our approach is specific to the problem at hand. It relies on the unique structure of the equation and makes no reference to any other techniques, with the exception of the geometry of unitary groups. In conclusion, a surprising fact comes to light. Namely, the mesoscopic dynamics "filters" through the (microscopic) Schrödinger dynamics as the latter turns out to be a clearly separable part, in fact an autonomous factor, of the evolution. This is a desirable result also from the physical standpoint.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
