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Active Hard Spheres in Infinitely Many Dimensions.
Thibaut Arnoulx de Pirey1, Gustavo Lozano2, Frédéric van Wijland1
1Universit de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France.
Physical Review Letters
|January 18, 2020
Summary
In infinite dimensions, active hard spheres exhibit solvable statistical mechanics, revealing motility-induced phase separation and vanishing propulsion at specific densities.
Area of Science:
- Statistical mechanics
- Soft matter physics
- Non-equilibrium systems
Background:
- Exact solutions for statistical-mechanical models with continuous degrees of freedom are rare, especially for non-equilibrium systems.
- Classical hard spheres in infinite dimensions offer a solvable model, providing a basis for exploring complex systems.
Purpose of the Study:
- To investigate the stationary properties of active hard spheres in infinite dimensions, far from equilibrium.
- To determine if dimensionality can simplify the analysis of active matter systems.
- To provide exact calculations for key properties like the structure factor and equation of state.
Main Methods:
- Utilizing an infinite-dimensional framework for active hard spheres.
- Calculating stationary state properties without relying on the Boltzmann distribution.
- Analyzing the structure factor and pressure (equation of state).
Main Results:
- Exact computation of the stationary state properties for active hard spheres in infinite dimensions.
- Demonstration of motility-induced phase separation.
- Determination of the critical crowding density where particle propulsion effectively ceases.
Conclusions:
- Infinite dimensionality is a powerful tool for analyzing non-equilibrium active matter systems.
- The study provides exact analytical results for the collective behavior of active hard spheres.
- The findings offer insights into phase separation and propulsion mechanisms in active matter.
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