Analytical canonical partition function of a quasi-one dimensional system of hard disks

Abstract

The exact canonical partition function of a hard disk system in a narrow quasi-one dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result the many body problem is reduced to solving two transcendental equations which can be easily done numerically. The longitudinal and transverse pressures in the whole density range are presented for three different pore widths. The transition from the solidlike zigzag to the liquidlike state is found to be quite sharp in the density scale but shows no genuine singularity. This transition is quantitatively described by the distribution of zigzag's windows through which disks exchange their positions across the pore.

arXiv comment11 pages, 7 figures

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Cited by in corpus (8)

• Comment on "Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system" [Phys. Rev. Research 2, 033351 (2020)]
• Equation of state of hard-disk fluids under single-file confinement
• Structural properties of hard-disk fluids under single-file confinement
• Kinetic temperature and pressure of an active Tonks gas
• Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement
• Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks
• Monte Carlo simulation of Hard-, Square-Well, and Square-Shoulder Disks in narrow channels
• Hard disks confined within a narrow channel