Session S30 - Mathematical Methods in Quantum Mechanics

Friday, July 16, 17:45 ~ 18:10 UTC-3

Spectrum of the Dirichlet Laplacian in sheared waveguides

Alessandra Verri

Universidade Federal de São Carlos, Brazil   -   alessandraverri@ufscar.br

Let $\Omega \subset \mathbb R^3$ be a waveguide which is obtained by translating a cross-section in a constant direction along an unbounded spatial curve. Consider $-\Delta_{\Omega}^D$ the Dirichlet Laplacian operator in $\Omega$. In this talk we show that, under the condition that the tangent vector of the reference curve admits a finite limit at infinity, the essential spectrum of $-\Delta_{\Omega}^D$ can be found. Furthermore, sufficient conditions to ensure the existence of a non-empty discrete spectrum for $-\Delta_{\Omega}^D$ are presented. In particular, we show that the number of discrete eigenvalues can be arbitrarily large since the waveguide is thin enough.

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