## View abstract

### 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   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak545c5b551631cda750431e7a8ca30993').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy545c5b551631cda750431e7a8ca30993 = '&#97;l&#101;ss&#97;ndr&#97;v&#101;rr&#105;' + '&#64;'; addy545c5b551631cda750431e7a8ca30993 = addy545c5b551631cda750431e7a8ca30993 + '&#117;fsc&#97;r' + '&#46;' + 'br'; var addy_text545c5b551631cda750431e7a8ca30993 = '&#97;l&#101;ss&#97;ndr&#97;v&#101;rr&#105;' + '&#64;' + '&#117;fsc&#97;r' + '&#46;' + 'br';document.getElementById('cloak545c5b551631cda750431e7a8ca30993').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy545c5b551631cda750431e7a8ca30993 + '\'>'+addy_text545c5b551631cda750431e7a8ca30993+'<\/a>';

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.