Stability analysis of inverse problems for coupled magnetic Schr\"odinger equations

TL;DR

This paper establishes a stability framework for simultaneously recovering multiple electromagnetic and coupling coefficients in a coupled Schrödinger system from partial boundary measurements, advancing inverse problem theory.

Contribution

It introduces a novel stability analysis for the inverse problem of determining multiple coefficients in coupled Schrödinger equations using finitely many boundary measurements.

Findings

Coefficients can be stably reconstructed with Hölder stability.

The method requires only finitely many boundary measurements.

The approach involves multiple initial condition modifications.

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 Schr\"odinger 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 H\"older stably retrieved by $(3d+2)$-times suitably changing the initial condition attached at the system.