Weakly Coupled Bound States in Quantum Waveguides

@inproceedings{Bulla1997WeaklyCB,
  title={Weakly Coupled Bound States in Quantum Waveguides},
  author={W. Bulla and Fritz Gesztesy and Walter Renger and Barry Simon},
  year={1997}
}
We study the eigenvalue spectrum of Dirichlet Laplacians which model quantum waveguides associated with tubular regions outside of a bounded domain. Intuitively, our principal new result in two dimensions asserts that any domain Ω obtained by adding an arbitrarily small “bump” to the tube Ω0 = R × (0, 1) (i.e., Ω Ω0, Ω ⊂ R2 open and connected, Ω = Ω0 outside a bounded region) produces at least one positive eigenvalue below the essential spectrum [π2 ,∞) of the Dirichlet Laplacian −∆Ω . For… CONTINUE READING
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