Stokes graphs of a quadratic differential related to a Rabi model, by René Langøen
![Stokes graph on sphere](https://www.uib.no/sites/w3.uib.no/files/styles/content_main/public/qz2-1_3d.png?itok=N5may7c6×tamp=1705316663)
Main content
Abstract: To study the behaviour of solutions to a second-order linear differential equation 𝑦″+𝑄(𝑧,𝑡)𝑦=0 one can associate the quadratic differential 𝑄(𝑧)𝑑𝑧2 on the punctured Riemann sphere and consider its Stokes graph. We consider an ODE related to a Rabi problem describing a light-atom interaction in physics. The associated quadratic differential is meromorphic with two finite poles. The integrability condition for this type of ODE under isomonodromic deformations is related to a non-linear second-order differential equation, known as Painlevé V. In my talk, I will explain a classification of the Stokes graphs according to the nature of the zeros of the meromorphic quadratic differential originated in the Rabi model. This is a joint work with I. Markina (University of Bergen) and A. Solynin (Texas Tech, USA).
![Stokes graph](https://www.uib.no/sites/w3.uib.no/files/styles/content_main/public/qz2-1_0.png?itok=U9BM5BSq×tamp=1705316978)
![Stokes graph on sphere](https://www.uib.no/sites/w3.uib.no/files/styles/content_main/public/qz2-1_3d_0.png?itok=pT1lelWh×tamp=1705316931)