Simulated annealing for topological solitons

Area of Science:

• Theoretical physics
• Computational physics
• Nonlinear dynamics

Background:

• Topological solitons are crucial in various nonlinear classical field theories.
• Finding soliton solutions typically involves solving static Euler-Lagrange equations numerically.
• Minimizing energy functionals is key to identifying the lowest energy field configurations.

Purpose of the Study:

• To explore simulated annealing as a direct energy minimization technique for finding topological solitons.
• To apply and evaluate the simulated annealing algorithm across different dimensions and field theories.
• To provide an alternative computational method for soliton research.

Main Methods:

• Direct minimization of energy functionals using a simulated annealing algorithm.
• Application to one-dimensional sine-Gordon model.
• Application to two-dimensional baby Skyrme model.
• Application to three-dimensional nuclear Skyrme model.

Main Results:

• The simulated annealing algorithm was successfully implemented for diverse nonlinear field theories.
• The method effectively identified field configurations corresponding to topological solitons.
• Results obtained via simulated annealing independently confirmed findings from standard numerical methods.

Conclusions:

• Simulated annealing provides a viable and effective alternative for finding topological solitons.
• This computational approach offers a direct method for energy functional minimization in field theory.
• The study validates simulated annealing as a robust tool for soliton research across multiple dimensions.