Discrete symmetries in periodic-orbit theory

Journal Article · Tue Aug 15 04:00:00 EDT 1989 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.40.2128· OSTI ID:5806783

Robbins, J M

The application of periodic-orbit theory to systems which possess a discrete symmetry is considered. A semiclassical expression for the symmetry-projected Green's function is obtained; it involves a sum over classical periodic orbits on a symmetry-reduced phase space, weighted by characters of the symmetry group. These periodic orbits correspond to trajectories on the full phase space which are not necessarily periodic, but whose end points are related by symmetry. If the symmetry-projected Green's functions are summed, the contributions of the unperiodic orbits cancel, and one recovers the usual periodic-orbit sum for the full Green's function. Several examples are considered, including the stadium billiard, a particle in a periodic potential, the Sinai billiard, the quartic oscillator, and the rotational spectrum of SF/sub 6/.

• Research Organization: Department of Physics, University of California, Berkeley, California 94720 (US)
• OSTI ID: 5806783
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 40:4; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ELECTRONIC EQUIPMENT
EQUIPMENT
FUNCTIONS
GREEN FUNCTION
MATHEMATICAL SPACE
MECHANICS
MOLECULES
OSCILLATORS
PHASE SPACE
QUANTUM MECHANICS
SPACE
SYMMETRY