Méndez-Bermúdez J A, Luna-Acosta G A, Seba P, Pichugin K N
Instituto de Física, Universidad Autónoma de Puebla, Apartado Postal J-48, México.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):046207. doi: 10.1103/PhysRevE.66.046207. Epub 2002 Oct 10.
We study classical and quantum scattering properties of particles in the ballistic regime in two-dimensional chaotic billiards that are models of electron- or micro-waveguides. To this end we construct the purely classical counterparts of the scattering probability (SP) matrix |S(n,m)|(2) and Husimi distributions specializing to the case of mixed chaotic motion (incomplete horseshoe). Comparison between classical and quantum quantities allows us to discover the purely classical dynamical origin of certain general as well as particular features that appear in the quantum description of the system. On the other hand, at certain values of energy the tunneling of the wave function into classically forbidden regions produces striking differences between the classical and quantum quantities. A potential application of this phenomenon in the field of microlasers is discussed briefly. We also see the manifestation of whispering gallery orbits as a self-similar structure in the transmission part of the classical SP matrix.
我们研究二维混沌台球中粒子在弹道 regime 下的经典和量子散射特性，二维混沌台球是电子或微波导的模型。为此，我们构建了散射概率（SP）矩阵|S(n,m)|²和专门针对混合混沌运动（不完全马蹄形）情况的胡西米分布的纯经典对应物。经典量与量子量之间的比较使我们能够发现系统量子描述中出现的某些一般以及特定特征的纯经典动力学起源。另一方面，在某些能量值下，波函数隧穿到经典禁区会导致经典量与量子量之间出现显著差异。简要讨论了这一现象在微激光器领域的潜在应用。我们还在经典SP矩阵的传输部分中看到了回音壁轨道作为一种自相似结构的表现。
