Low lying eigenvalues of randomly curved quantum waveguides

摘要: Abstract We consider the negative Dirichlet Laplacian on an infinite waveguide embedded in R 2 , and finite segments thereof. The is a perturbation of periodic strip terms sequence independent identically distributed random variables which influence curvature. derive explicit lower bounds first eigenvalue randomly curved small coupling (i.e. weak disorder) regime. This allows us to estimate probability low lying eigenvalues, tool relevant context Anderson localization for Schrodinger operators.