Hamiltonian Monodromy in a Tavis-Cummings System with an $A_2$ Singularity
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914479511437312 |
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| author | Efstathiou, Konstantinos Gutierrez-Guillen, Gabriela Jocelyn Mardešić, Pavao Sugny, Dominique |
| author_facet | Efstathiou, Konstantinos Gutierrez-Guillen, Gabriela Jocelyn Mardešić, Pavao Sugny, Dominique |
| contents | Singular Lagrangian fibrations arising from three-degree-of-freedom integrable Hamiltonian systems remain largely unexplored. While several results describe the global structure of large classes of systems with two degrees of freedom, only a few examples are understood in higher dimensions. We present a three-degree-of-freedom system derived from the two-spin Tavis-Cummings model whose singular Lagrangian fibration exhibits a topology that has not been observed in other physical models. We show that the most degenerate singular fiber is homeomorphic to $\mathbf{S}^2\times\mathbf{S}^1$ with a singularity of $A_2$ type. We further describe the bifurcation diagram and the global topology of the fibration, and we compute its Hamiltonian monodromy. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Monodromy in a Tavis-Cummings System with an $A_2$ Singularity Efstathiou, Konstantinos Gutierrez-Guillen, Gabriela Jocelyn Mardešić, Pavao Sugny, Dominique Mathematical Physics Symplectic Geometry 37J35, 53D20, 70H06, 70H33 Singular Lagrangian fibrations arising from three-degree-of-freedom integrable Hamiltonian systems remain largely unexplored. While several results describe the global structure of large classes of systems with two degrees of freedom, only a few examples are understood in higher dimensions. We present a three-degree-of-freedom system derived from the two-spin Tavis-Cummings model whose singular Lagrangian fibration exhibits a topology that has not been observed in other physical models. We show that the most degenerate singular fiber is homeomorphic to $\mathbf{S}^2\times\mathbf{S}^1$ with a singularity of $A_2$ type. We further describe the bifurcation diagram and the global topology of the fibration, and we compute its Hamiltonian monodromy. |
| title | Hamiltonian Monodromy in a Tavis-Cummings System with an $A_2$ Singularity |
| topic | Mathematical Physics Symplectic Geometry 37J35, 53D20, 70H06, 70H33 |
| url | https://arxiv.org/abs/2604.14835 |