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Curvature-induced symmetry breaking in nonlinear Schrodinger models
Gaididei1, Mingaleev, Christiansen
1Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine.
Summary
Curvature and nonlinearity in oscillator chains cause symmetry breaking, favoring asymmetric states. Bending traps nonlinear excitations by reducing their energy, impacting stability.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Theoretical physics
Background:
- Nonlinear oscillators exhibit complex behaviors.
- Curvature can influence system dynamics.
- Symmetry breaking is a key phenomenon in physical systems.
Purpose of the Study:
- Investigate the interplay of curvature and nonlinearity in oscillator chains.
- Analyze the conditions for symmetry breaking.
- Examine the effect of bending on nonlinear excitations and stability.
Main Methods:
- Theoretical analysis of a curved chain of nonlinear oscillators.
- Investigation of stationary states and their energies.
- Application of stability criteria, including the Vakhitov-Kolokolov criterion.
Main Results:
- Curvature and nonlinearity induce symmetry breaking, favoring asymmetric stationary states.
- Localized state energy decreases with increasing curvature, indicating bending acts as a trap.
- Violation of the Vakhitov-Kolokolov stability criterion observed due to softening of the Peierls internal mode.
Conclusions:
- Bending is an effective mechanism for trapping nonlinear excitations in curved nonlinear oscillator chains.
- The study reveals a novel pathway for instability driven by the softening of internal modes.
- Findings have implications for understanding localized phenomena in curved nonlinear systems.
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