Thermal equilibration in a one-dimensional damped harmonic crystal.

Area of Science:

• Physics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• The study investigates thermal equilibration in a 1D harmonic crystal immersed in a viscous medium.
• Initially, the system is far from thermal equilibrium with zero displacements and random velocities.
• In conservative systems, kinetic and potential energies oscillate and stabilize at half the initial kinetic energy.

Purpose of the Study:

• To analyze the features of the unsteady thermal equilibration process in a damped harmonic crystal.
• To understand how external damping affects the energy dynamics compared to conservative systems.
• To determine the long-time asymptotic behavior of kinetic and potential energies.

Main Methods:

• Analytical investigation of the system's dynamics.
• Modeling the viscous environment using damping.
• Numerical calculations to verify analytical results.

Main Results:

• The presence of damping introduces a two-stage energy decay process.
• Stage 1 (underdamped): Oscillations decay exponentially.
• Stage 2 (always present): Oscillations vanish, leading to power-law decay (t^{-3/2} for potential energy, t^{-5/2} for kinetic energy).

Conclusions:

• External damping qualitatively alters thermal equilibration dynamics.
• At large times, potential energy dominates over kinetic energy.
• Analytical and numerical findings are consistent.