Disorder, Chaos and Correlations in Quantum Systems

介观物理学在过去几年中取得了重大进展。小无序系统系综中样本波动的统计方法推动了理论的进步。随着系统的尺寸越来越小，最终它们接近电子平均自由程。然后电子的运动变成了弹道运动。另一方面，由于复杂的几何结构，这种运动仍然可能是混沌的。这样的系统在许多方面与显示量子混沌的其他系统（原子或核）相似。对于分析计算而言，由于附加的系综平均，无序系统比混沌弹道系统更简单。这项研究的想法是使用无序系统作为研究量子混沌的实验室。在扩散状态下，我们打算推导出关系式并发展出可以推广到一般情况的分析方法。对与量子混沌密切相关的孤立环中持续电流问题和孤立金属晶粒的磁化率问题也将进行理论研究。我们将考虑电子之间的相互作用，因为现有的单电子理论与实验有很大的分歧。介观物理学是一个非常新的领域，它处理基础物理学中的基本问题，但对微电子学有重要的影响。本研究将从理论上处理介观物理学中的一些问题。特别是，本研究将研究这些系统中量子混沌的开始。显然，除了它的基本重要性之外，微电子系统变得混乱或不稳定的条件也是计算机和通信行业感兴趣的。

The field of mesoscopic physics has had significant progress during the past few years. The theoretical progress has been driven by the statistical approach to sample fluctuations in the ensemble of small disordered systems. As the sizes of the systems are made smaller and smaller, eventually they approach the electron mean free path. Then the motion of an electron becomes ballistic. On the other hand, due to the complex geometry, this motion can still be chaotic. Such a system is similar in many respects to other systems (atomic or nuclear) which display quantum chaos. For analytical calculations disordered systems turn out to be simpler than chaotic ballistic ones because of the additional ensemble averaging. The idea of this research is to use disordered systems as a laboratory for the investigation of quantum chaos. In a diffusive regime we plan to derive relations and develop analytical methods which can be extended to general cases. Theoretical studies will also be carried out on problems of persistent currents in isolated rings and the magnetic susceptibility of isolated metallic grains - problems closely connected to quantum chaos. We will take into account interactions between electrons since existing one-electron theories are in substantial disagreement with experiment. %%% The field of mesoscopic physics is a very current one which deals with basic problems in fundamental physics and yet has important ramifications for microelectronics. The present research will theoretically deal with a number of problems in mesoscopic physics. In particular, the research will study the onset of quantum chaos in these systems. Clearly, besides its fundamental importance, the conditions under which a microelectronic system becomes chaotic, or unstable, is of interest to the computer and communications industry.