Density and energy relaxation in an open one-dimensional system

Area of Science:

• Statistical Physics
• Computational Physics
• Soft Matter Physics

Background:

• Master equations are crucial for modeling complex systems.
• Excluded volume interactions and external perturbations significantly affect particle dynamics.
• Open systems allow for fluctuations in particle number, adding complexity.

Purpose of the Study:

• To propose and numerically solve a new master equation for interacting random walkers in an open system.
• To investigate the influence of excluded volume interactions, external potentials, and particle exchange on walker dynamics.
• To analyze the energy relaxation behavior under different perturbation models.

Main Methods:

• Development of a novel master equation to describe the system.
• Numerical solution of the master equation.
• Simulation of random walkers with excluded volume interactions (single-file system).
• Inclusion of particle exchange with a bath (open system).
• Application of two distinct external potentials: inverse (1/r) and inverse sixth power (1/r6).

Main Results:

• The model exhibits interesting dynamics in walker density and total energy.
• Highly nonexponential energy relaxation is observed when system size is comparable to the perturbation range.
• Stretched exponential and logarithmic time dependencies of energy relaxation occur in this regime.
• Particle exchange with the bath significantly reduces the nonexponentiality of the relaxation function.

Conclusions:

• The proposed master equation effectively captures complex dynamics of interacting random walkers.
• External potentials and system size play critical roles in energy relaxation behavior.
• Open system dynamics, particularly particle exchange, can regularize nonexponential relaxation patterns.