Related Experiment Videos
Validity of the semiclassical periodic orbit approximation in the two- and three-disk problems
1Nordita, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark.
Chaos (Woodbury, N.Y.)
|January 1, 1992
Summary
Classical cycle expansion accurately predicts high-energy resonances in quantum scattering from disks. However, corrections for low-energy resonances in the two-disk problem are insufficient, indicating semiclassical predictions will fail.
Area of Science:
- Quantum mechanics
- Mathematical physics
- Scattering theory
Background:
- Classical cycle expansion approximates high-lying resonances in quantum scattering.
- Deviations exist for the lowest resonances in scattering problems involving circular hard disks.
Purpose of the Study:
- Investigate leading corrections from creeping paths to the cycle expansion.
- Analyze the two- and three-disk scattering problems.
- Determine the validity of semiclassical predictions for low-lying resonance poles.
Main Methods:
- Constructing leading corrections from creeping paths.
- Applying the cycle expansion to two- and three-disk scattering.
- Estimating the magnitude of these corrections.
Main Results:
- Classical cycle expansion shows good agreement for high-lying resonances.
- Noticeable deviations observed for the lowest resonances.
- Calculated corrections are too small to explain these deviations.
Conclusions:
- Semiclassical predictions for low-lying resonance poles are expected to fail for two- and three-disk scattering problems.
- Further theoretical developments are needed to accurately describe low-lying resonances.