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Graph Limits of Thin Network Systems

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Quantum Waveguides

Part of the book series: Theoretical and Mathematical Physics ((TMP))

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Abstract

In contrast to the previous chapters, the present one deals with networks of tubes. If the latter are thin, a simple description of such systems is obtained through the concept of a quantum graph. The requirement of probability current conservation at the graph vertices leaves a lot of freedom and one can ask whether all such couplings can be obtained by squeezing networks of finite-diameter tubes. An affirmative answer is given here for tubes with Neumann-type boundaries. For Dirichlet boundaries the limit is substantially different and it is illustrated here on a particular case.

... there is a risk of being lost in the maze of tangled structures and crevasses, sometimes reminiscent of jumbled colonnades, sometimes of petrified geysers.

Stanislaw Łem, Solaris

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Correspondence to Pavel Exner .

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Exner, P., Kovařík, H. (2015). Graph Limits of Thin Network Systems. In: Quantum Waveguides. Theoretical and Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-18576-7_8

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