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Low-frequency discrete breathers in long-range systems without on-site potential
Yoshiyuki Y Yamaguchi1, Yusuke Doi2
1Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
Physical Review. E
|July 18, 2018
Summary
Long-range couplings enable low-frequency discrete breathers, crucial for nonlinear dynamics, by opening a necessary frequency gap. This mechanism is effective where short-range couplings fail, offering new possibilities for localized energy transport.
Area of Science:
- Nonlinear Dynamics
- Condensed Matter Physics
- Lattice Vibrations
Background:
- Discrete breathers are localized nonlinear modes in periodic structures.
- Their existence typically requires on-site potentials or specific coupling conditions.
- Low-frequency breathers are particularly interesting for energy localization and transport.
Purpose of the Study:
- To propose and investigate a mechanism for generating low-frequency discrete breathers.
- To explore the role of long-range couplings in realizing these breathers without on-site potentials.
- To determine the conditions under which such breathers can be formed and sustained.
Main Methods:
- Theoretical analysis under periodic boundary conditions and the limit of large population.
- Investigating the impact of coupling functions (long-range vs. short-range) on frequency band gaps.
- Numerical analysis to confirm the existence, spatial localization, and stability of the discrete breathers.
Main Results:
- Long-range couplings universally open a frequency gap below the linear eigenfrequency band, irrespective of coupling function.
- Short-range couplings do not open this essential gap.
- Low-frequency discrete breathers were confirmed to exist, be spatially localized, and stable for long-range couplings.
Conclusions:
- Long-range couplings provide a viable mechanism for realizing low-frequency discrete breathers without on-site potentials.
- The universal gap opening by long-range couplings is key to their formation.
- This finding expands the possibilities for controlling nonlinear localized modes in various physical systems.
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