Next Analysis and PDE seminar
- René Langøen, University of Bergen
- Title: The direct monodromy problem and isomonodromic deformations for the Rabi model.
Abstract: We discuss the local and global solutions of the Rabi model in Garnier form, a linear system of first order differential equations, with complex rational coefficients. The analytic continuation of the local solutions are described by a monodromy group, which gives a matrix representation of the fundamental group of the punctured Riemann sphere. A detailed geometric description of linear systems of first order differential equations is given, in terms of a local family of connection forms on a principal bundle. The geometric description reveals the Frobenius integrability conditions, which are used to obtain necessary and sufficient conditions for an isomonodromic deformation of the Rabi model.