Understanding quantum scattering properties in terms of purely classical dynamics: two-dimensional open chaotic billiards

• Published in: Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics Vol. 66; no. 4 Pt 2; p. 046207
• Main Authors: Méndez-Bermúdez, J A, Luna-Acosta, G A, Seba, P, Pichugin, K N
• Format: Journal Article
• Language: English
• Published: United States 01-10-2002
• ISSN: 1539-3755; 1063-651X; 1095-3787
• DOI: 10.1103/PhysRevE.66.046207

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.