论文标题
关于复合量子系统中密度的复杂行为
On the complex behaviour of the density in composite quantum systems
论文作者
论文摘要
在本文中，我们研究了粒子的存在的可能性是如何分布在复合效率系统的两个部分之间的。我们发现概率的差异取决于以惊人的方式，并显示了该分布的模式。我们讨论了后者的主要特征，并通过分析解释我们理解的那些特征。特别是，我们证明这是一种非扰动性能，我们发现了一个大/小的耦合恒定双重性。我们还发现并研究了可能将我们的问题与非线性经典动力学的某些方面联系起来的功能，例如共振的存在和对系统状态的敏感依赖性。我们表明，后者确实具有与经典力学相似的起源：扰动系列中小分母的外观。受KAM定理的证明的启发，我们能够通过引入消除这些小分母的能量中的截断来解决这个问题。我们还制定了一些猜想，这些猜想目前无法证明，但数值实验可以支持。
In this paper, we study how the probability of presence of a particle is distributed between the two parts of a composite fermionic system. We uncover that the difference of probability depends on the energy in a striking way and show the pattern of this distribution. We discuss the main features of the latter and explain analytically those that we understand. In particular, we prove that it is a non-perturbative property and we find out a large/small coupling constant duality. We also find and study features that may connect our problem with certain aspects of non linear classical dynamics, like the existence of resonances and sensitive dependence on the state of the system. We show that the latter has indeed a similar origin than in classical mechanics: the appearance of small denominators in the perturbative series. Inspired by the proof of KAM theorem, we are able to deal with this problem by introducing a cut-off in energies that eliminates these small denominators. We also formulate some conjectures that we are not able to prove at present but can be supported by numerical experiments.
