Hard core run and tumble particles on a one-dimensional lattice

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Condensed Matter Theory

Background:

• Run and tumble particles are fundamental models for active matter.
• Understanding their collective behavior on lattices is crucial for complex systems.

Purpose of the Study:

• To investigate the large-scale behavior of hard core run and tumble particles on a 1D lattice.
• To analyze the system's steady-state properties and hydrodynamic transport coefficients.

Main Methods:

• Mapping the run and tumble model to a mass transfer model with fluctuating directed bonds.
• Employing mean-field approximation for high spin-flip rates.
• Utilizing a coalescence-fragmentation model for low spin-flip rates.

Main Results:

• Calculated the steady-state single-site mass distribution for different spin-flip rates.
• Determined hydrodynamic coefficients of diffusivity and conductivity.
• Demonstrated the violation of the Einstein relation in both high and low spin-flip rate regimes.

Conclusions:

• The study provides insights into the non-equilibrium statistical mechanics of active particles.
• It highlights the importance of considering the nongradient nature of the process for accurate hydrodynamic calculations.
• The findings contribute to the understanding of transport phenomena in complex particle systems.