Letters in Mathematical Physics· 2026Q1
Spectral properties of the Dirichlet Laplacian in twisted and sheared waveguides
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- Q1SCImago
- 2026year
Short summary
Discrete eigenvalues emerge in 3D waveguides with twisted and sheared cross-sections, revealing a link between geometry and spectral behavior.
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Key points
- Analyzes the Dirichlet Laplacian in unbounded 3D waveguides with twisted and sheared cross-sections.
- Identifies conditions for the emergence of discrete eigenvalues due to geometric twisting.
- Demonstrates that shearing alone can enrich the spectral structure of straight waveguides.
- Highlights the interplay between waveguide geometry and spectral properties.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In this work, we analyze the Dirichlet Laplacian $$-\Delta _{\Omega }^D$$ - Δ Ω D in an unbounded waveguide $$\Omega \subset \mathbb {R}^3$$ Ω ⊂ R 3 , where the cross section is translated in a constant direction and rotated along a spatial line. We focus on the effects of twisting on the spectrum, discussing conditions under which discrete eigenvalues emerge. Our results highlight the interplay between geometry and spectral properties, showing that shearing can induce a richer spectral structure even in straight waveguides.
The authors' abstract, as published at the source. Letters in Mathematical Physics, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics