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Torus doubling resonances and breather stability
1Physics Department, Clarkson University, Potsdam, New York 13699-5820, USA. schulman@clarkson.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
Discrete breathers in doped alkali halides exhibit torus doubling, a bifurcation phenomenon. These localized excitations can persist for extended periods, explaining anomalous luminescence decay.
Area of Science:
- Solid-state physics
- Nonlinear dynamics
- Materials science
Background:
- Discrete breathers are localized nonlinear excitations in periodic structures.
- Doped alkali halides provide a system where discrete breathers can arise.
- Anomalous luminescence decay suggests underlying complex physical phenomena.
Purpose of the Study:
- To investigate the properties of discrete breathers in doped alkali halides.
- To analyze the torus doubling bifurcation in nonlinear modes.
- To understand the long-term survival and physical implications of two-frequency breather excitations.
Main Methods:
- Analysis of nonlinear modes and phase space structures.
- Numerical simulations to observe breather dynamics.
- Theoretical investigation of phonon resonances and their impact on localization.
Main Results:
- Observed torus doubling: a period-doubling bifurcation in the phase space of nonlinear modes.
- Demonstrated practical localization of two-frequency breathers despite theoretical delocalization due to phonon resonances.
- Showcased breather survival for over 10^9 characteristic time scales.
Conclusions:
- Torus doubling is a key phenomenon in the dynamics of discrete breathers.
- Two-frequency breathers, though theoretically susceptible to phonon resonances, exhibit remarkable stability in doped alkali halides.
- The long-lived nature of these localized excitations explains observable physical effects like anomalous luminescence decay.
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