Doklady Mathematics

, Volume 92, Issue 1, pp 514–518 | Cite as

Spectra of three-dimensional cruciform and lattice quantum waveguides

  • F. L. BakharevEmail author
  • S. G. Matveenko
  • S. A. Nazarov
Mathematical Physics


It is shown that the discrete spectrum of the Dirichlet problem for the Laplacian on the union of two mutually perpendicular circular cylinders consists of a single eigenvalue, while the homogeneous problem with a threshold value of the spectral parameter has no bounded solutions. As a consequence, an adequate one-dimensional model of a square lattice of thin quantum waveguides is presented and the asymptotic behavior of the spectral bands and lacunas (zones of wave transmission and deceleration) and the oscillatory processes they generate is described.


Dirichlet Problem Discrete Spectrum DOKLADY Mathematic Dirichlet Condition Oscillatory Process 
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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  • F. L. Bakharev
    • 1
    Email author
  • S. G. Matveenko
    • 1
    • 2
  • S. A. Nazarov
    • 1
    • 3
    • 4
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.St. Petersburg BranchNational Research University “Higher School of Economics,”St. PetersburgRussia
  3. 3.St. Petersburg State Polytechnical UniversitySt. PetersburgRussia
  4. 4.Institute of Mechanical Engineering ProblemsRussian Academy of SciencesSt. PetersburgRussia

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