Quantum geometry of the rotating shallow water model
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918291177472000 |
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| author | Ganeshan, Sriram Dorsey, Alan T. |
| author_facet | Ganeshan, Sriram Dorsey, Alan T. |
| contents | The rotating shallow water equations (RSWE) are a mainstay of atmospheric and oceanic modeling, and their wave dynamics has close analogues in settings ranging from two-dimensional electron gases to active-matter fluids. While recent work has emphasized the topological character of RSWE wave bands, here we develop a complementary quantum-geometric description by computing the full quantum geometric tensor (QGT) for the linearized RSWE on an $f$-plane. The QGT unifies two pieces of band geometry: its real part defines a metric that quantifies how rapidly wave polarization changes with parameters, while its imaginary part is the Berry curvature that controls geometric phases and topological invariants. We obtain compact, symmetry-guided expressions for all three bands, highlighting the transverse structure of the metric and the monopole-like Berry curvature that yields Chern numbers for the Poincaré bands. Finally, we describe a feasible route to probing this geometry in rotating-tank experiments via weak, time-periodic parametric driving. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10695 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum geometry of the rotating shallow water model Ganeshan, Sriram Dorsey, Alan T. Fluid Dynamics Mesoscale and Nanoscale Physics Atmospheric and Oceanic Physics The rotating shallow water equations (RSWE) are a mainstay of atmospheric and oceanic modeling, and their wave dynamics has close analogues in settings ranging from two-dimensional electron gases to active-matter fluids. While recent work has emphasized the topological character of RSWE wave bands, here we develop a complementary quantum-geometric description by computing the full quantum geometric tensor (QGT) for the linearized RSWE on an $f$-plane. The QGT unifies two pieces of band geometry: its real part defines a metric that quantifies how rapidly wave polarization changes with parameters, while its imaginary part is the Berry curvature that controls geometric phases and topological invariants. We obtain compact, symmetry-guided expressions for all three bands, highlighting the transverse structure of the metric and the monopole-like Berry curvature that yields Chern numbers for the Poincaré bands. Finally, we describe a feasible route to probing this geometry in rotating-tank experiments via weak, time-periodic parametric driving. |
| title | Quantum geometry of the rotating shallow water model |
| topic | Fluid Dynamics Mesoscale and Nanoscale Physics Atmospheric and Oceanic Physics |
| url | https://arxiv.org/abs/2601.10695 |