Time-dependent properties of run-and-tumble particles. II. Current fluctuations

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Condensed Matter Theory

Background:

• Run-and-tumble particles (RTPs) are a key model for active matter, exhibiting complex dynamics on lattices.
• Understanding steady-state current fluctuations is crucial for characterizing transport properties in non-equilibrium systems.
• Previous studies have explored RTPs, but a comprehensive analysis of current fluctuations and scaling laws is needed.

Purpose of the Study:

• To investigate steady-state current fluctuations in two models of hardcore run-and-tumble particles (RTPs) on a 1D lattice.
• To determine the scaling behavior of current fluctuations with time and system size.
• To explore universal scaling laws for particle mobility in the dilute and slow tumbling limits.

Main Methods:

• Theoretical analysis of two hardcore RTP models on a periodic 1D lattice: standard RTPs and a long-ranged lattice gas (LLG).
• Calculation of cumulative current fluctuations and their dependence on time (T) and lattice size (L).
• Derivation of scaling functions for current fluctuations and particle mobility, validated against simulation results.

Main Results:

• Current fluctuations exhibit crossover from subdiffusive (α=1/2) to diffusive (α=1) behavior with time.
• A universal scaling curve for scaled bond-current fluctuations W(y) was identified, independent of model details.
• A scaling law for scaled mobility H(ψ) was found in the dilute, slow tumbling limit, though model-dependent.

Conclusions:

• The study reveals universal scaling properties in current fluctuations and mobility for RTPs on a lattice.
• The theoretical predictions show excellent agreement with simulation results for both models.
• This work provides a deeper understanding of transport phenomena in active matter systems.