Carleman estimate for infinite cylindrical quantum domains and application to inverse problems

Abstract

We consider the inverse problem of determining the time independent scalar potential of the dynamic Schrödinger equation in an infinite cylindrical domain, from one Neumann boundary observation of the solution. Assuming that this potential is known outside some fixed compact subset of the waveguide, we prove that it may be Lipschitz stably retrieved by choosing the Dirichlet boundary condition of the system suitably. Since the proof is by means of a global Carleman estimate designed specifically for the Schrödinger operator acting in an unbounded cylindrical domain, the Neumann data is measured on an infinitely extended subboundary of the cylinder.

References in corpus (4)

• Inverse boundary value problem for the dynamical heterogeneous Maxwell system
• Stable Determination of Time-Dependent Scalar Potential From Boundary Measurements in a Periodic Quantum Waveguide
• An inverse anisotropic conductivity problem induced bytwisting a homogeneous cylindrical domain
• Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains

Cited by in corpus (10)

• Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary
• Logarithmic Stability for Coefficients Inverse Problem of Coupled Schrödinger Equations
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• The inverse problem of two-state quantum systems with non-adiabatic static linear coupling
• Stable recovery of a non-compactly supported coefficient of a Schrödinger equation on an infinite waveguide
• Stability estimate for a partial data inverse problem for the convection-diffusion equation
• Stable recovery of non-compactly supported electromagnetic potentials in unbounded domain
• Hölder stable determination of a quantum scalar potential in unbounded cylindrical domains
• Determination of non-compactly supported electromagnetic potentials in unbounded closed waveguide