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Dynamical trapping and chaotic scattering of the harmonically driven barrier
Florian R N Koch1, Florian Lenz, Christoph Petri
1Physikalisches Institut, Universität Heidelberg, Philosophenweg 12, 69120 Heidelberg, Germany. florian.koch@physi.uni-heidelberg.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2008
Summary
This study reveals dynamical trapping in a driven square potential barrier, leading to chaotic scattering and trajectory stickiness. Classical resonances mimic quantum tunneling, but with distinct origins.
Area of Science:
- Nonlinear Dynamics
- Classical Mechanics
- Chaos Theory
Background:
- Investigates the complex behavior of a driven square potential barrier.
- Focuses on the classical nonlinear dynamics of oscillating systems.
Purpose of the Study:
- To analyze the classical nonlinear dynamics of a driven square potential barrier.
- To understand phenomena like dynamical trapping and chaotic scattering.
Main Methods:
- Detailed analysis of classical nonlinear dynamics.
- Phase space analysis to identify stable islands.
- Examination of unstable periodic orbits within KAM structures.
Main Results:
- Observed dynamical trapping associated with stable phase space islands.
- Identified the driven barrier as a chaotic scatterer due to unstable periodic orbits.
- Demonstrated stickiness of scattering trajectories near the stable island.
- Transmission function resembles quantum tunneling resonances but arises classically.
Conclusions:
- Classical nonlinear dynamics can exhibit phenomena analogous to quantum effects.
- Dynamical trapping and chaotic scattering are key features of this system.
- The observed resonances have a classical origin, distinct from quantum tunneling.
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