Everlasting effect of initial conditions on single-file diffusion

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Complex Systems

Background:

• Single-file systems, characterized by one-dimensional transport where particles cannot overtake each other, exhibit unique dynamic behaviors.
• Understanding the influence of initial particle configurations is crucial for predicting system evolution and transport properties.
• The Einstein relation typically describes equilibrium dynamics, but its applicability in non-equilibrium or memory-dependent systems requires investigation.

Purpose of the Study:

• To investigate how different initial conditions affect the dynamics of a tagged particle in a one-dimensional single-file system.
• To analyze the impact of initial particle arrangements on transport coefficients and the validity of the Einstein relation.
• To explore the long-time behavior and memory effects within the single-file model.

Main Methods:

• Simulation of a tagged particle interacting with point Brownian particles with hard-core potentials in an infinite 1D channel.
• Comparison of two distinct initial conditions: equal inter-particle spacing and uniform density distribution.
• Analysis of mean-square displacement, correlation functions, and transport coefficients, including diffusivity, using methods like the Jepsen line.

Main Results:

• Distinct initial conditions lead to measurable differences in the mean-square displacement and correlation functions of the tagged particle.
• The violation of the Einstein relation is observed and shown to be dependent on the specific initial state and averaging method (time vs. ensemble).
• Transport coefficients, such as diffusivity, are demonstrated to be state-dependent, influenced by the initial configuration.

Conclusions:

• Initial conditions play a deterministic role in the long-time dynamics of single-file systems, imparting a form of 'system memory'.
• Unlike equilibrium thermal systems, single-file models do not necessarily forget their initial state, highlighting non-ergodic behavior.
• The study underscores the importance of considering initial state preparation when characterizing transport phenomena in confined, interacting particle systems.