Higher-Rank Connections and Deformed Schrödinger Operators
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| Format: | Preprint |
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2026
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| _version_ | 1866913147175043072 |
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| author | Baerman, Jonah Grassi, Alba Ravazzini, Giovanni |
| author_facet | Baerman, Jonah Grassi, Alba Ravazzini, Giovanni |
| contents | We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions decay at each singularity, leading to a rich structure of boundary value problems. We derive the weakest quantization conditions compatible with decaying behavior at both singularities, and formulate these conditions in terms of the associated monodromy data. In doing so, we prove the quantization conditions predicted by the topological string/spectral theory duality for a family of deformed Schrödinger equations. More generally, our results point to a hierarchy of spectral problems interpolating between the minimal conditions studied here and the maximally decaying boundary conditions of the $N$-particle quantum Toda chain. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Higher-Rank Connections and Deformed Schrödinger Operators Baerman, Jonah Grassi, Alba Ravazzini, Giovanni Mathematical Physics High Energy Physics - Theory Spectral Theory Exactly Solvable and Integrable Systems We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions decay at each singularity, leading to a rich structure of boundary value problems. We derive the weakest quantization conditions compatible with decaying behavior at both singularities, and formulate these conditions in terms of the associated monodromy data. In doing so, we prove the quantization conditions predicted by the topological string/spectral theory duality for a family of deformed Schrödinger equations. More generally, our results point to a hierarchy of spectral problems interpolating between the minimal conditions studied here and the maximally decaying boundary conditions of the $N$-particle quantum Toda chain. |
| title | Higher-Rank Connections and Deformed Schrödinger Operators |
| topic | Mathematical Physics High Energy Physics - Theory Spectral Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2605.20338 |