Hard disks confined within a narrow channel
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918379404656640 |
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| author | Brader, J. M. Di Bernardo, E. Tschopp, S. M. |
| author_facet | Brader, J. M. Di Bernardo, E. Tschopp, S. M. |
| contents | We employ inhomogeneous integral equation theory to investigate the equilibrium properties of hard disks confined to a channel of width $L$ by hard parallel walls. If the channel width is narrowed below two disk diameters, then the system enters a quasi one-dimensional regime for which the particles cannot move past each other. In the limit when $L$ is equal to one particle diameter the system reduces to the one-dimensional bulk along the center of the channel. We study first the dimensional crossover properties of the inhomogeneous Percus-Yevick (PY) integral equation as $L$ is reduced and then investigate the behaviour of a quasi one-dimensional system as the packing of the particles is increased for a fixed value of $L$. We find that the inhomogeneous PY equation is highly accurate for situations of quasi one-dimensional confinement and that it predicts the onset of a structural transition to a zigzag state at higher packing. The excellent performance of this integral equation method and the ease with which it handles confinement-induced dimensional crossover is a consequence of the improved resolution which comes from treating explicitly the inhomogeneous two-body correlation functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hard disks confined within a narrow channel Brader, J. M. Di Bernardo, E. Tschopp, S. M. Soft Condensed Matter Statistical Mechanics We employ inhomogeneous integral equation theory to investigate the equilibrium properties of hard disks confined to a channel of width $L$ by hard parallel walls. If the channel width is narrowed below two disk diameters, then the system enters a quasi one-dimensional regime for which the particles cannot move past each other. In the limit when $L$ is equal to one particle diameter the system reduces to the one-dimensional bulk along the center of the channel. We study first the dimensional crossover properties of the inhomogeneous Percus-Yevick (PY) integral equation as $L$ is reduced and then investigate the behaviour of a quasi one-dimensional system as the packing of the particles is increased for a fixed value of $L$. We find that the inhomogeneous PY equation is highly accurate for situations of quasi one-dimensional confinement and that it predicts the onset of a structural transition to a zigzag state at higher packing. The excellent performance of this integral equation method and the ease with which it handles confinement-induced dimensional crossover is a consequence of the improved resolution which comes from treating explicitly the inhomogeneous two-body correlation functions. |
| title | Hard disks confined within a narrow channel |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2601.16642 |