Correlation functions and their universal connection during an extremely slow equilibration process.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Non-equilibrium Dynamics

Background:

• Investigating equilibration processes in complex systems is crucial for understanding their long-term behavior.
• Many systems exhibit transient states that significantly delay or alter the approach to equilibrium.

Purpose of the Study:

• To analyze the equilibration dynamics of a 1D lattice with transverse motions and an external magnetic field.
• To characterize the stability and properties of a metastable transient state.
• To examine heat transport mechanisms in both transient and equilibrium states.

Main Methods:

• Simulating a one-dimensional lattice model with transverse motions and an external magnetic field.
• Analyzing spatiotemporal energy correlations and global heat current autocorrelation.
• Comparing correlation functions in metastable transient and ergodic equilibrium states.

Main Results:

• The system reaches a highly stable metastable state with extremely long relaxation times, diverging faster than exponentially.
• Spatiotemporal energy correlations and heat current autocorrelation differ significantly between transient and equilibrium states.
• The transient state suggests normal heat diffusion and conduction, while the equilibrium state shows super diffusion and anomalous conduction.

Conclusions:

• The observed metastable state possesses exceptional stability compared to other systems.
• A general relation connecting energy and heat current correlations holds true in both metastable and equilibrium states.
• The universality of this correlation relation is extended to non-equilibrium transient dynamics.