Abstract

The classical motion of particles in external fields is frequently chaotic although deterministic within the classical limit. Studying the quantum mechanical behavior of such systems amounts to the problematics of quantum chaos. Quantum chaos manifests itself primarily in the statistical properties of the energy-level arrays of such systems. However, the typical objects under consideration are systems of the type billiards with rigid walls. This paper studies the calculated energy levels of the transverse motion of relativistic electrons in the axial-channeling regime along the [100] direction of the silicon crystal which is described as motion in the smooth potential well. The nearest-level spacing distributions as well as the spectral rigidity are studied for the range of parameters where electron motion is chaotic within the classical limit. Both these characteristics demonstrate agreement with quantum-chaos-theory predictions.

中文翻译：

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动态混沌条件下硅晶体中引导电子的横向运动能级的统计特性

摘要

粒子在外场中的经典运动虽然在经典极限内是确定性的，但经常是混沌的。研究此类系统的量子力学行为相当于解决量子混沌问题。量子混沌主要表现为此类系统的能级阵列的统计特性。然而，所考虑的典型对象是具有刚性壁的台球类型的系统。本文研究了相对论电子在轴向沟道区沿硅晶体[100]方向横向运动的计算能级，该方向被描述为光滑势阱中的运动。研究了电子运动在经典极限内是混沌的参数范围的最近能级间距分布以及光谱刚度。