The Kibble-Zurek mechanism in a subcritical bifurcation

Area of Science:

• Nonlinear dynamics
• Condensed matter physics
• Complex systems

Background:

• Topological defects are crucial in various physical systems.
• The Kibble-Zurek (KZ) mechanism explains defect formation during phase transitions.
• Understanding defect freezing dynamics in non-equilibrium systems is essential.

Purpose of the Study:

• To investigate the freezing dynamics of topological defects.
• To test the Kibble-Zurek (KZ) mechanism in a subcritical tri-stable system.
• To characterize different out-of-equilibrium regimes and their dynamics.

Main Methods:

• Utilized a one-dimensional quintic complex Ginzburg-Landau equation.
• Employed quasistatic and quenched studies to predict critical exponents.
• Analyzed defect number and spatial correlation functions for correlation length.
• Differentiated adiabatic, impulse, and free relaxation regimes.

Main Results:

• Critical exponents for the KZ mechanism and KZ-scaling regime were predicted and validated.
• Correlation length in the KZ freezing regime was corroborated by defect count and spatial correlation.
• Three distinct out-of-equilibrium regimes (adiabatic, impulse, free relaxation) were identified.
• The impulse regime was found to coincide with a rapid exponential increase in the order parameter.

Conclusions:

• The study validates the Kibble-Zurek mechanism in a complex, non-equilibrium system.
• Defect freezing dynamics are well-characterized by the KZ mechanism and scaling laws.
• The identified out-of-equilibrium regimes offer insights into system behavior far from equilibrium.