Nonreciprocal Coupling Induced Self-Assembled Localized Structures

Area of Science:

• Physics
• Nonlinear Dynamics
• Condensed Matter Physics

Background:

• Coupled oscillator chains typically propagate energy via waves, pulses, and fronts.
• Nonreciprocal coupling significantly alters these wave dynamics.

Purpose of the Study:

• To investigate the nonlinear wave dynamics in chains with nonreciprocal nearest-neighbor coupling.
• To understand the emergent phenomena arising from such coupling, specifically localized structures and traveling waves.

Main Methods:

• Development of a prototype model for nonlinear chains with nonreciprocal coupling.
• Analytical determination of the phase diagram.
• Numerical simulations to validate analytical findings.

Main Results:

• Nonreciprocal coupling induces a convective instability between stable and unstable equilibria.
• Increased coupling leads to the emergence of a propagative pattern, identified as a traveling wave.
• Characterization of the pattern wavelength as a function of the coupling strength.
• Analytical phase diagram matches numerical simulation results.

Conclusions:

• Nonreciprocal coupling is a key mechanism for generating self-assembled localized structures and traveling waves in nonlinear chains.
• The study provides a framework for understanding emergent wave phenomena in systems with asymmetric interactions.