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Entrainment of a driven oscillator as a dynamical phase transition
Alex Dickson1, S M Ali Tabei, Aaron R Dinner
1James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
Large deviation theory reveals oscillator entrainment as a phase transition. This study numerically solves large deviation functions, showing a diverging current derivative and strong state coupling in the entrainment region.
Area of Science:
- Physics
- Nonlinear Dynamics
- Statistical Mechanics
Background:
- Large deviation theory provides a framework for studying dynamical phase transitions.
- Oscillator entrainment to external forces is a key phenomenon in nonlinear systems.
Purpose of the Study:
- To describe oscillator entrainment as a phase transition using large deviation theory.
- To numerically obtain exact solutions for the large deviation function of a driven oscillator model.
Main Methods:
- Utilized large deviation theory and numerical methods.
- Analyzed a discrete, finite model of an oscillator under periodic forcing.
- Calculated exact solutions for the large deviation function.
Main Results:
- Identified oscillator entrainment as a phase transition in a joint space-time representation.
- Observed divergence in the first derivative of the expectation value of the current for large system sizes.
- Found strong coupling between ground and excited states within the entrainment region.
Conclusions:
- Large deviation theory offers a powerful tool for understanding complex dynamical phenomena like oscillator entrainment.
- The study elucidates the nature of the entrainment transition and its relation to the system's spectral properties.
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