The 2D Chern-Simons-Schr{ö}dinger system reduced to 1D
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908787634339840 |
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| author | Rougerie, Nicolas Yang, Qiyun |
| author_facet | Rougerie, Nicolas Yang, Qiyun |
| contents | We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schr{ö}dinger matter field coupled to a Chern-Simons gauge field. We derive an effective 1D equation by adding a strongly anisotropic trapping potential (wave-guide) acting on the Schr{ö}dinger field, and tracing out the tight confinement direction. The effective dynamics in the loose direction of the wave-guide turns out to be governed by the classical 1D quintic NLS equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The 2D Chern-Simons-Schr{ö}dinger system reduced to 1D Rougerie, Nicolas Yang, Qiyun Analysis of PDEs Mesoscale and Nanoscale Physics Quantum Gases Mathematical Physics We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schr{ö}dinger matter field coupled to a Chern-Simons gauge field. We derive an effective 1D equation by adding a strongly anisotropic trapping potential (wave-guide) acting on the Schr{ö}dinger field, and tracing out the tight confinement direction. The effective dynamics in the loose direction of the wave-guide turns out to be governed by the classical 1D quintic NLS equation. |
| title | The 2D Chern-Simons-Schr{ö}dinger system reduced to 1D |
| topic | Analysis of PDEs Mesoscale and Nanoscale Physics Quantum Gases Mathematical Physics |
| url | https://arxiv.org/abs/2508.21464 |