Vortex kinetics of conserved and nonconserved On models

Area of Science:

• Physics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Phase-ordering models describe systems transitioning to ordered states.
• Vortex dynamics are crucial in understanding these transitions.
• Conserved and nonconserved models exhibit distinct behaviors.

Purpose of the Study:

• To develop an analytical method for predicting vortex motion in conserved and nonconserved phase-ordering models.
• To compute speed and position distribution functions for annihilating point vortices.
• To validate the analytical method through numerical simulations.

Main Methods:

• Heuristic scaling arguments were employed to derive analytical predictions.
• Numerical simulations of the conserved and nonconserved O(2) model in 2D were performed.
• Speed and position distribution functions were computed and compared.

Main Results:

• The analytical method accurately predicted speed distributions for nonconserved models.
• Numerical results for nonconserved models aligned with theoretical predictions.
• The method accurately predicted large-speed tails for conserved models but struggled with small speeds.
• Position distribution functions showed good agreement with analytical results for both models.

Conclusions:

• The developed analytical method is effective for predicting vortex motion, particularly position distributions.
• The method shows promise for extension to models with scalar order parameters.
• Further refinement is needed for accurate prediction of small-speed vortex dynamics in conserved systems.