Spectrum of the Schr\"odinger operator in a perturbed periodically   twisted tube
  We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum. 
Pavel Exner and Hynek Kova\v{r}\'ik