Canonical partition function and distance dependent correlation functions of a quasi-one-dimensional system of hard disks
arXiv:2307.05995 · doi:10.1016/j.molliq.2023.122572
Abstract
The canonical NLT partition function of a quasi-one dimensional (q1D) one-file system of equal hard disks [J. Chem Phys. 153, 144111 (2020)] provides an analytical description of the thermodynamics and ordering in this system (a pore) as a function of linear density Nd/L where d is the disk diameter. We derive the analytical formulae for the distance dependence of the translational pair distribution function and the distribution function of distances between next neighbor disks, and then demonstrate their use by calculating the translational order in the pore. In all cases, the order is found to be of a short range and to exponentially decay with the disks' separation. The correlation length presented for different pore widths and densities shows a non-monotonic dependence with a maximum at Nd/L=1 and tends to the 1D value for a vanishing pore width. The results indicate a special role of this density when the pore length L is equal exactly to N disk diameters. A comparison between the theoretical results for an infinite system and the results of a molecular dynamics simulation for a finite system with periodic boundary conditions is presented and discussed.
Change of License to CC-BY. arXiv admin note: substantial text overlap with arXiv:2206.05980
References in corpus (12)
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- The 1D interacting Bose gas in a hard wall box
- Understanding the ideal glass transition: Lessons from an equilibrium study of hard disks in a channel
- Glass-like behavior of a hard-disk fluid confined to a narrow channel
- Structural properties of hard disks in a narrow tube
- Landscapes, dynamic heterogeneity and kinetic facilitation in a simple off-lattice model
- Correlation lengths in quasi-one-dimensional systems via transfer matrices
- Transverse excitations and zigzag transition in quasi-1D hard-disk system
- Equation of state of hard-disk fluids under single-file confinement
- Comment on "Kosterlitz-Thouless-type caging-uncaging transition in a quasi-one-dimensional hard disk system" [Phys. Rev. Research 2, 033351 (2020)]
- Analytical canonical partition function of a quasi-one dimensional system of hard disks
- Critical behavior of hard squares in strong confinement