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arXiv · 2604.14835

Hamiltonian Monodromy in a Tavis-Cummings System with an $A_2$ Singularity

Konstantinos Efstathiou·Gabriela Jocelyn Gutierrez-Guillen·Pavao Mardešić·Dominique Sugny
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Abstract

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.

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Konstantinos Efstathiou, Gabriela Jocelyn Gutierrez-Guillen, Pavao Mardešić, Dominique Sugny. 2026-04-16. Hamiltonian Monodromy in a Tavis-Cummings System with an $A_2$ Singularity. https://arxiv.org/abs/2604.14835

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