Energy relaxation in nonlinear one-dimensional lattices

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Statistical mechanics

Background:

• Thermalized one-dimensional nonlinear arrays, specifically Fermi-Pasta-Ulam (FPU) type, are investigated.
• Understanding energy relaxation in such systems is crucial for various physical phenomena.

Purpose of the Study:

• To investigate the energy relaxation pathways in thermalized one-dimensional nonlinear FPU-type arrays coupled to a zero-temperature reservoir.
• To analyze the influence of harmonic and anharmonic interactions on the relaxation dynamics.
• To identify the role of localized modes and breathers in the long-time relaxation behavior.

Main Methods:

• Simulations of thermalized one-dimensional nonlinear FPU-type arrays with damping forces at the ends.
• Analysis of energy decay and mode evolution in harmonic, anharmonic, and mixed interaction systems.
• Observation of relaxation dynamics upon injection of localized excitations to study breather behavior.

Main Results:

• Harmonic arrays exhibit sequential phonon decay, with lower-frequency modes relaxing first.
• Purely anharmonic arrays show degradation of high-energy modes, leaving residual energy in low-frequency localized modes.
• Mixed harmonic-anharmonic arrays display extremely slow relaxation at long times due to persistent high-frequency stationary breathers.

Conclusions:

• The energy relaxation pathway in FPU-type arrays is strongly dependent on the nature of inter-site interactions (harmonic vs. anharmonic).
• Localized modes and breathers play a significant role in hindering complete energy dissipation, leading to persistent energy in the system.
• The presence of breathers, especially in mixed systems, dictates the slow, long-time relaxation dynamics.