Poincare Husimi representation of eigenstates in quantum billiards

Journal Article · Wed Sep 01 00:00:00 EDT 2004 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.70.036204· OSTI ID:20636595

Baecker, A ^[1]; Fuerstberger, S ^[2]; Schubert, R ^[3]

---

1. Institut fuer Theoretische Physik, TU Dresden, D-01062 Dresden (Germany)
2. Abteilung Theoretische Physik, Universitaet Ulm Albert-Einstein-Allee 11, D-89069 Ulm (Germany)
3. Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW (United Kingdom)

For the representation of eigenstates on a Poincare section at the boundary of a billiard different variants have been proposed. We compare these Poincare Husimi functions, discuss their properties, and based on this select one particularly suited definition. For the mean behavior of these Poincare Husimi functions an asymptotic expression is derived, including a uniform approximation. We establish the relation between the Poincare Husimi functions and the Husimi function in phase space from which a direct physical interpretation follows. Using this, a quantum ergodicity theorem for the Poincare Husimi functions in the case of ergodic systems is shown.

• OSTI ID: 20636595
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 3 Vol. 70; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHAOS THEORY
EIGENFUNCTIONS
EIGENSTATES
PHASE SPACE
STATISTICAL MECHANICS