Universal large deviations for the tagged particle in single-file motion.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Nonlinear Dynamics

Background:

• Single-file motion describes particle transport in confined systems where particles cannot overtake each other.
• Understanding tagged particle dynamics is crucial for characterizing transport properties in such systems.
• Previous work shows subdiffusive or diffusive behavior depending on individual particle dynamics.

Purpose of the Study:

• To compute the exact large deviation function for tagged particle displacement in single-file motion.
• To investigate the universality of tagged particle motion, independent of underlying particle dynamics.

Main Methods:

• Analysis of a one-dimensional gas of point particles with hard-core interactions.
• Focus on the motion of a single tagged particle starting from equilibrium initial conditions.
• Exact computation of the large deviation function for particle displacement.

Main Results:

• The tagged particle displacement exhibits subdiffusive behavior for diffusive individual particle dynamics.
• The tagged particle displacement shows diffusive behavior for ballistic individual particle dynamics.
• The computed large deviation function for tagged particle displacement is universal.

Conclusions:

• The large deviation function for tagged particle displacement in single-file motion is independent of the specific particle dynamics.
• This universality simplifies the characterization of transport in these constrained systems.
• The findings provide a fundamental insight into statistical mechanics of confined systems.