On the correlation lengths of confined spheres in a cylindrical pore

We investigate the structural correlations of hard spheres confined within a narrow cylindrical pore in the quasi-one-dimensional regime, where interactions are restricted to nearest neighbors. Using a Laplace-space formulation of the radial distribution function (RDF), we determine the correlation lengths and oscillation frequencies associated with its long-distance decay. In addition to the global RDF, we analyze transverse-resolved RDFs that account for the positions of particle pairs across the pore cross section. While these observables are associated with the same underlying pole spectrum, their residues depend on the transverse configuration and can vanish due to symmetry. As a result, different particle-pair configurations may be governed by different leading poles and display different correlation lengths and oscillation frequencies. In particular, the global RDF does not always reflect the longest-ranged correlation found in the system. We examine how this behavior depends on density and confinement. In the strong-confinement limit, the system approaches the Tonks-gas behavior at finite pressure, and the differences between the RDFs disappear.