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- W1653498265 abstract "The aim of the theory of quantum waveguides is the description of motion of electrons in two-or three-dimensional small channels, tubes or layers of crystalline matter of high purity - for example, one or several films or lines of a semiconducting substance epitaxed on a wafer. The mesoscopic lengthscale of such structures allows an experimentator to shape them as requested, yet on the other hand, structures on this scale are open for quantum effects. In fact, it has been shown in experiments that changes in the shape of such structures have an influence on their conductivity properties, see, for example, the physical literature cited in [DE], whose extensive bibliography provides a good overview of work on the subject in general at the same time. Mathematically speaking, we are interested in the impact of a changing geometry on the spectral properties of a Schrodinger operator in this geometry, a challenging and attractive task. Various models constituted by (minus) the Laplacian operator on a domain of ℝ2 or ℝ3 with Dirichlet boundary conditions have been investigated in this context, see [BGRS, DE, ES, ESTV, EV]. One has considered the bending of a strip as in Figure 1, opening a window be-tween two adjacent strips as in Figure 2 or bulging a strip as in Figure 3 and analogous situations in three dimensions. In all cases, the existence of a number of bound states with eigenvalues below the essential spectrum emerged from it during the deformation could be proven. Thus, the conjecture put up in [DE], that a random deformation, e. g. a random denting or bulging, of a quantum waveguide strip on its full infinite length will cause infinitely many bound states or dense pure point spectrum at the bottom of the spectrum, is well motivated.In a joint paper ([KS]),P.Stollmann and the author were able to deal with suche a model of a quantum waveguide irregularly deformed over its full length;one of the results is the verification of the mentioned conjecture." @default.
- W1653498265 created "2016-06-24" @default.
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- W1653498265 date "1999-01-01" @default.
- W1653498265 modified "2023-09-27" @default.
- W1653498265 title "Localization and Lifshitz tails for Random Quantum Waveguides" @default.
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- W1653498265 doi "https://doi.org/10.1007/978-3-0348-8745-8_25" @default.
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