International Journal of Mathematics and Mathematical Sciences· 2012Q3
Inverse Problem for a Curved Quantum Guide
- 975citations
- Q3SCImago
- 2012year
Short summary
This paper establishes uniqueness results for reconstructing the curvature of a quantum guide in 2D or 3D space using spectral data or a bootstrapping method.
AI-generated from the title and abstract; the full text is not read.
Key points
- Uniqueness results for inverse problems are provided for curved quantum guides.
- The quantum guide is defined in R^n (n=2, 3) with an asymptotically straight reference curve.
- Reconstruction of curvature is possible using spectral data or a bootstrapping method.
- The Dirichlet Laplacian operator is central to the analysis.
AI-generated from the title and abstract; the full text is not read.
Abstract
We consider the Dirichlet Laplacian operator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mo>−</mml:mo><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow></mml:math>on a curved quantum guide in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:msup><mml:mi>ℝ </mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>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.
The authors' abstract, as published at the source. International Journal of Mathematics and Mathematical Sciences, 2012 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics