Thermalization in Asymmetric Harmonic Chains

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• The symmetry of interparticle interaction potentials (IIP) is crucial for thermodynamic and transport properties of solids.
• Asymmetry and nonlinearity in IIP are often interconnected, making it difficult to study their isolated effects.
• Understanding thermalization dynamics is key to predicting material behavior under various conditions.

Purpose of the Study:

• To investigate the isolated effect of IIP asymmetry on thermalization dynamics.
• To introduce and analyze a one-dimensional asymmetric harmonic (AH) model to decouple asymmetry from nonlinearity.
• To explore thermalization in a system with combined IIP asymmetry and nonlinearity.

Main Methods:

• Development of a one-dimensional asymmetric harmonic (AH) model with asymmetry but no nonlinearity.
• Conducting extensive numerical simulations to study thermalization time (Teq).
• Analyzing the relationship between thermalization time and perturbation strength in both asymmetric and asymmetric-nonlinear models.

Main Results:

• A power-law relationship between thermalization time and perturbation strength was confirmed for the AH chain.
• The observed exponent in the AH chain is larger than the previously known inverse-square law.
• Matthiessen's rule effectively estimated thermalization time when symmetric quartic nonlinearity was added to the AH model.

Conclusions:

• Interparticle interaction potential asymmetry plays a distinct role in thermalization dynamics, separate from nonlinearity.
• Asymmetry enhances higher-order effects and governs relaxation dynamics in solids.
• The findings provide new insights into the fundamental mechanisms of thermalization in condensed matter systems.