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Test of semiclassical amplitudes for quantum ray-splitting systems
1Sysdeco GIS AS, P.O. Box 433, 3604 Kongsberg, Norway. Achim.Kohler@gis.sysdeco.no
Summary
We calculated ray-splitting orbits in quantum systems. Including reflection and transmission is crucial for accurate density of states calculations in these complex billiards.
Area of Science:
- Quantum chaos
- Statistical mechanics
- Mathematical physics
Background:
- Ray-splitting billiards are complex dynamical systems.
- Understanding their density of states is key to quantum chaos.
- Previous semiclassical methods often simplified ray-splitting dynamics.
Purpose of the Study:
- To compute semiclassically and numerically the weights of ray-splitting orbits.
- To validate semiclassical predictions against numerical simulations.
- To assess the importance of reflection and transmission coefficients in ray-splitting systems.
Main Methods:
- Semiclassical analysis of ray-splitting orbits.
- Numerical computation of the density of states.
- Comparison of semiclassical and numerical results for rectangular and annular billiards.
Main Results:
- Excellent agreement between semiclassical and numerical results.
- Demonstrated the significance of ray-splitting orbits.
- Quantified the impact of reflection and transmission coefficients.
Conclusions:
- Semiclassical methods accurately predict the density of states in ray-splitting billiards.
- Reflection and transmission coefficients of non-Newtonian orbits are essential for semiclassical accuracy.
- This work validates and refines semiclassical approaches for complex quantum systems.