The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating w.r.t. the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincides with the spectrum of the straight tube of the same cross-section and that the discrete spectrum is not empty. MSC2000: 81Q10; 58J50; 53A04.

Cyclotron resonance spectra of 2D electrons in HgTe/Cd x Hg 1−x Te (0 1 3) quantum well (QW) heterostructures with inverted band structure have been thoroughly studied in quasiclassical magnetic fields versus the electron concentration varied using the persistent photoconductivity effect. The cyclotron mass is shown to increase with QW width in contrast to QWs with normal band structure. The measured values of cyclotron mass are shown to be systematically less than those calculated using the 8 × 8 Kane model with conventional set of HgTe and CdTe material parameters. In quantizing pulsed magnetic fields (Landau level filling factor less than unity) up to 45 T, both intraband (CR) and interband magnetoabsorption have been studied at radiation wavelengths 14.8 and 11.4 μm for the first time. The results obtained are compared with the allowed transition energies between Landau levels in the valence and conduction bands calculated within the same model, the calculated energies being again systematically less (by 3-14%) than the observed optical transition energies.