Stability estimate for the aligned magnetic field in a periodic quantum waveguide from dirichlet-to-neumann map

TL;DR

This paper establishes a stability estimate for identifying the aligned magnetic field in a periodic quantum waveguide using boundary measurements, advancing inverse problem techniques in quantum physics.

Contribution

It provides a new H"older stability estimate for the magnetic Schr"odinger equation in a periodic waveguide based on the Dirichlet-to-Neumann map, utilizing geometrical optics solutions.

Findings

Proved a H"older stability estimate for the magnetic field.

Used geometrical optics solutions to analyze the inverse problem.

Enhanced understanding of boundary inverse problems in quantum waveguides.

Abstract

In this article, we study the boundary inverse problem of determining the aligned magnetic fiaeld appearing in the magnetic Schr\"odinger equation in a periodic quantum cylindrical waveguide. Provided that the Dirichlet-to-Neumann map of the magnetic Schr\"odinger equation. We prove a Holder stability estimate with respect to the Dirichlet-to-Neumann map, by means of the geometrical optics solutions of the magnetic Schrodinger equation.