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Spectral properties of soft quantum waveguides

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arxiv 2006.15071 v3 pith:PCUGW2C2 submitted 2020-06-26 math.SP math-phmath.MPquant-ph

Pavel Exner This is my paper · ORCID
classification math.SPmath-phmath.MPquant-ph
keywords channelpotentialprofilequantumsoftstraightalongasymptotically
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We consider a soft quantum waveguide described by a two-dimensional Schr\"odinger operators with an attractive potential in the form of a channel of a fixed profile built along an infinite smooth curve which is not straight but it is asymptotically straight in a suitable sense. Using Birman-Schwinger principle we show that the discrete spectrum of such an operator is nonempty if the potential well defining the channel profile is deep and narrow enough. Some related problems are also mentioned.

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  1. Spectral Analysis of a Soft Quantum Waveguide Coupled to a Massive Quantum Scalar Field

    math-ph 2026-07 conditional novelty 6.0 of 10

    For a Nelson-type Hamiltonian on a soft quantum waveguide, the essential spectrum of the curved guide is a half-line whose threshold combines the straight-guide ionization threshold and the one-boson mass; a negative ...

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