Structural properties of hard-disk fluids under single-file confinement

The structural properties of confined single-file hard-disk fluids are studied analytically by means of a mapping of the original system onto a one-dimensional mixture of non-additive hard rods, the mapping being exact in the polydisperse limit. Standard statistical-mechanical results are used as a starting point to derive thermodynamic and structural properties of the one-dimensional mixture, where the condition that all particles have the same chemical potential must be taken into account. Analytical results are then provided for the $n$th neighbor probability distribution function, the radial distribution function, and the structure factor, a very good agreement being observed upon comparison with simulation data from the literature. Moreover, we have analyzed the scaling form for the disappearance of defects in the zigzag configuration for high pressure, and have obtained the translational correlation length and the structural crossover in the oscillation frequency for asymptotically large distances.