کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6415119 | 1334946 | 2014 | 35 صفحه PDF | دانلود رایگان |
We consider a twisted quantum waveguide, i.e. a domain of the form Ωθ:=rθÏÃR where ÏâR2 is a bounded domain, and rθ=rθ(x3) is a rotation by the angle θ(x3) depending on the longitudinal variable x3. We investigate the nature of the essential spectrum of the Dirichlet Laplacian Hθ, self-adjoint in L2(Ωθ), and consider related scattering problems. First, we show that if the derivative of the difference θ1âθ2 decays fast enough as |x3|ââ, then the wave operators for the operator pair (Hθ1,Hθ2) exist and are complete. Further, we concentrate on appropriate perturbations of constant twisting, i.e. θâ²=βâε with constant βâR, and ε which decays fast enough at infinity together with its first derivative. In that case the unperturbed operator corresponding to ε is an analytically fibered Hamiltonian with purely absolutely continuous spectrum. Obtaining Mourre estimates with a suitable conjugate operator, we prove, in particular, that the singular continuous spectrum of Hθ is empty.
Journal: Journal of Functional Analysis - Volume 266, Issue 1, 1 January 2014, Pages 1-35