Transient diffusion and thermal processes in a finite one-dimensional harmonic crystal.

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Thermodynamics

Background:

• Understanding thermal transport and diffusion in crystalline structures is fundamental to materials science.
• Periodic systems offer unique behaviors due to their inherent symmetry and wave propagation characteristics.

Purpose of the Study:

• To investigate the dynamic response of a one-dimensional harmonic crystal to an instantaneous homogeneous thermal perturbation.
• To derive exact solutions for thermal and diffusive characteristics, including particle velocity and displacement dispersion.
• To analyze the emergent phenomena of thermal echoes and quasi-periodic recurrence in diffusion.

Main Methods:

• Analytical derivation of exact solutions for particle velocity and displacement dispersion.
• Analysis of thermal and diffusive characteristics under homogeneous thermal perturbation.
• Investigation of spatial and ensemble mean squared displacements.

Main Results:

• Exact solutions for kinetic temperature and particle displacement dispersion were obtained.
• Quasi-periodic recurrence of thermal and diffusion processes was observed, with recurrence intervals linked to sound wave propagation.
• A 'thermal echo' phenomenon was identified, characterized by sharp peaks in kinetic temperature.
• Diffusion characteristics showed large-scale temporal changes and near-complete returns to initial states.
• Significant differences were found between spatial and ensemble mean squared displacements.

Conclusions:

• The study confirms quasi-periodic recurrence and 'thermal echo' effects in harmonic crystals subjected to thermal perturbations.
• The findings highlight the distinct nature of spatial versus ensemble diffusion in such systems.
• This research provides insights into fundamental thermal transport mechanisms in periodic condensed matter systems.