Inverse Problem for a Curved Quantum Guide

TL;DR

This paper addresses the inverse problem of reconstructing the curvature of a curved quantum guide in two and three dimensions using spectral data or boot-strapping methods, contributing to quantum geometry analysis.

Contribution

It provides new uniqueness results for the inverse problem of determining curvature from spectral observations in curved quantum guides.

Findings

Uniqueness of curvature reconstruction established

Spectral data can determine the guide's curvature uniquely

Boot-strapping method effective for inverse problem

Abstract

In this paper, we consider the Dirichlet Laplacian operator -{\Delta} on a curved quantum guide in R n (n = 2, 3) with an asymptotically straight reference curve. We give uniqueness results for the inverse problem associated to the reconstruction of the curvature by using either observations of spectral data or a boot-strapping method. keywords: Inverse Problem, Quantum Guide, Curvature