Hard Disks in Narrow Channels

TL;DR

This paper investigates the thermodynamic and dynamical properties of hard disks confined in narrow channels, revealing singularities in pressure, collision frequency, and Lyapunov exponents related to channel width and boundary effects.

Contribution

It provides a theoretical and numerical analysis of how confinement alters the behavior of hard disk gases, highlighting singularities and boundary-induced configurations.

Findings

Pressure and collision frequency show singularities at twice the disk diameter.

Maximum Lyapunov exponent exhibits similar singular behavior.

High-density states are dominated by boundary-influenced solid-like configurations.

Abstract

The thermodynamic and dynamical behavior of a gas of hard disks in a narrow channel is studied theoretically and numerically. Using a virial expansion we find that the pressure and collision frequency curves exhibit a singularity at a channel width corresponding to twice the disk diameter. As expected, the maximum Lyapunov exponent is also found to display a similar behavior. At high density these curves are dominated by solid-like configurations which are different from the bulk ones, due to the channel boundary conditions.