Thermal fluctuation for the time-dependent Ginzburg-Landau simulation

Area of Science:

• Physics
• Computational Physics
• Materials Science

Background:

• Time-dependent Ginzburg-Landau simulations are crucial for modeling dynamic processes in condensed matter.
• Accurately quantifying thermal fluctuations is essential for understanding system behavior.
• Existing methods may not fully capture thermal effects in nonconserved systems.

Purpose of the Study:

• To develop a theoretical framework for evaluating thermal fluctuations in nonconserved systems.
• To propose a formula for thermal fluctuation magnitude based on fundamental principles.
• To validate the proposed formula through numerical simulations.

Main Methods:

• Utilizing ensemble theory and the fluctuation-dissipation relation.
• Developing a treatment for thermal fluctuation evaluation in nonconserved systems.
• Performing numerical simulations to verify the derived formula.

Main Results:

• A novel formula for thermal fluctuation in nonconserved systems is presented.
• The magnitude of thermal fluctuation is shown to depend on coarse-grained volume.
• Curvature of the free-energy function at thermal equilibrium is identified as a key factor influencing fluctuation magnitude.

Conclusions:

• The proposed method provides a valid approach for assessing thermal fluctuations in nonconserved systems.
• The findings offer insights into the interplay between system size, free energy landscape, and thermal noise.
• This work contributes to more accurate modeling of dynamic phenomena in various physical systems.