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Partitioning the phase space in a natural way for scattering systems
1Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
This study introduces a new method for creating symbolic dynamics in open systems, using a driven inverted Gaussian model relevant to laser-atom interactions. The approach effectively captures the unstable dynamics observable by external observers.
Area of Science:
- * Physics
- * Nonlinear Dynamics
- * Quantum Optics
Background:
- * Open systems present challenges in dynamical analysis due to interactions with their environment.
- * Symbolic dynamics offers a powerful framework for simplifying complex system behavior.
- * Laser-atom interactions are often modeled using potentials like the driven inverted Gaussian.
Purpose of the Study:
- * To demonstrate a novel procedure for constructing symbolic dynamics in open systems.
- * To apply this procedure to the driven inverted Gaussian model for laser-atom interactions.
- * To analyze the effectiveness of symbolic dynamics from an asymptotic observer's perspective.
Main Methods:
- * Application of a recent symbolic dynamics construction procedure.
- * Utilization of the driven inverted Gaussian model potential.
- * Analysis of the Poincaré map and scattering functions.
Main Results:
- * The constructed symbolic dynamics naturally aligns with partitions of the Poincaré map.
- * The resulting branching tree from symbolic dynamics matches that derived from scattering functions.
- * The procedure approximates the globally unstable part of the chaotic invariant set.
Conclusions:
- * Symbolic dynamics provides a useful tool for understanding open systems, particularly in laser-atom interactions.
- * The method's validity is confirmed by its agreement with scattering data from an asymptotic viewpoint.
- * The approximation inherent in the method excludes certain complex dynamical features like KAM islands.
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