Stability analysis of inverse problems for coupled magnetic Schrödinger equations

Abstract

We consider the inverse coefficient problem of simultaneously determining the space dependent electromagnetic potential, the zero-th order coupling term and the first order coupling vector of a two-state Schrödinger equation in a bounded domain of ${\mathbb{R}}^d$, $d\ge 2$, from finitely many partial boundary measurements of the solution. We prove that these $3d+3$ unknown scalar coefficients can be Hölder stably retrieved by $(3d+2)$-times suitably changing the initial condition attached at the system.