Weakly Coupled Bound States in Quantum Waveguides

  title={Weakly Coupled Bound States in Quantum Waveguides},
  author={W. Bulla and Fritz Gesztesy and Walter Renger and Barry Simon},
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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Showing 1-10 of 17 references

Existence of bound states in quantum waveguides under weak conditions

  • W. Renger, W. Bulla
  • Lett. Math. Phys. 35
  • 1995
3 Excerpts

Exis tence theorems for trapped modes

  • M. Levitin, D. Vassiliev
  • J . Fluid Mech .
  • 1994

Bound states in quantum waveguides of a slowly decaying curvature

  • P. Exner
  • J. Math. Phys. 34
  • 1993

Curvature vs

  • P. Duclos, P. Exner
  • thickness in quantum waveguides, Czech. J. Phys…
  • 1992
1 Excerpt

th ickness in q u a n t u m waveguides , Czech

  • P. Exner
  • J . Phys .
  • 1991

thickness in quantum waveguides

  • P. Exner
  • Czech . J . Phys .
  • 1991

Lower bounds to bound state energies in bent tubes

  • M. S. Ashbaugh, P. Exner
  • Phys. Lett. A 150
  • 1990
1 Excerpt

Bound states in curved quantum waveguides

  • P. Exner, P. Šeba
  • J. Math. Phys. 30
  • 1989

Stovi ~ ek , O n existence of a bound s tate in a n L - shaped Czech

  • P.
  • J . Math . Phys .
  • 1989

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