René Langøen: Stokes graph of a quadratic differential related to a Rabi model

Abstract:

To study a behaviour of solutions to a second-order linear differential equation \(y'' + Q(z, t) y = 0\) one can associate the quadratic differential \(Q(z) dz^2\) on the punctured Riemann sphere and consider its Stokes graph. We consider ODE related to the 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).