Open Access
Volume 57, Number 6, November-December 2023
Page(s) 3251 - 3273
Published online 29 November 2023
  1. J. Aguilar and J.-M. Combes, A class of analytic perturbations for one-body Schrödinger Hamiltonians. Comm. Math. Phys. 22 (1971) 269–279. [CrossRef] [MathSciNet] [Google Scholar]
  2. S. Albeverio, C. Cacciapuoti and D. Finco, Coupling in the singular limit of thin quantum waveguides, J. Math. Phys. 48 (2007) 032103, 21. [CrossRef] [MathSciNet] [Google Scholar]
  3. Y. Avishai, D. Bessis, B.G. Giraud and G. Mantica, Quantum bound states in open geometries. Phys. Rev. B 15 (1991) 8028–8034. [CrossRef] [PubMed] [Google Scholar]
  4. F.L. Bakharev and S.A. Nazarov, Criteria for the absence and existence of bounded solutions at the threshold frequency in a junction of quantum waveguides. St. Petersburg Math. J. 32 (2021) 955–973. [CrossRef] [MathSciNet] [Google Scholar]
  5. F.L. Bakharev, S.G. Matveenko and S.A. Nazarov, Spectra of three-dimensional cruciform and lattice quantum waveguides. Dokl. Math. 92 (2015) 514–518. [CrossRef] [MathSciNet] [Google Scholar]
  6. F.L. Bakharev, S.G. Matveenko and S.A. Nazarov, The discrete spectrum of cross-shaped waveguides. St. Petersburg Math. J. 28 (2017) 171–180. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Balslev and J.-M. Combes, Spectral properties of many-body Schrödinger operators with dilatation-analytic interactions. Comm. Math. Phys. 22 (1971) 280–294. [CrossRef] [MathSciNet] [Google Scholar]
  8. J.-P. Berenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114 (1994) 185–200. [CrossRef] [Google Scholar]
  9. G. Berkolaiko and P. Kuchment, Introduction to Quantum Graphs. Vol. 186. American Mathematical Society (AMS), Providence, RI (2013). [Google Scholar]
  10. M.S. Birman and M.Z. Solomjak, Spectral Theory of Selfadjoint Operators in Hilbert space. Mathematics and its Applications (Soviet Series). D. Reidel Publishing Co., Dordrecht (1987). [CrossRef] [Google Scholar]
  11. A.-S. Bonnet-Ben Dhia, L. Chesnel and V. Pagneux, Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem. Proc. R. Soc. A 474 (2018) 20180050. [CrossRef] [Google Scholar]
  12. E.N. Bulgakov, P. Exner, K.N. Pichugin and A.F. Sadreev, Multiple bound states in scissor-shaped waveguides. Phys. Rev. B 66 (2002) 155109. [CrossRef] [Google Scholar]
  13. C. Cacciapuoti, Graph-like asymptotics for the Dirichlet Laplacian in connected tubular domains. Anal. Geom. Number Theory 2 (2017) 25–58. [Google Scholar]
  14. C. Cacciapuoti and P. Exner, Nontrivial edge coupling from a Dirichlet network squeezing: the case of a bent waveguide. J. Phys. A Math. Theor. 40 (2007) f511–g523. [Google Scholar]
  15. P. Exner and H. Kovařík, Quantum Waveguides. Springer (2015). [CrossRef] [Google Scholar]
  16. I.M. Gelfand, Expansion in characteristic functions of an equation with periodic coefficients. Dokl. Akad. Nauk SSSR 73 (1950) 1117–1120. [Google Scholar]
  17. D. Grieser, Spectra of graph neighborhoods and scattering. Proc. Lond. Math. Soc. 97 (2008) 718–752. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Grieser, Thin tubes in mathematical physics, global analysis and spectral geometry, in Analysis on Graphs and its Applications. Selected papers based on the INI programme, Cambridge, UK, January 8–June 29, 2007 (2008) 565–593. [Google Scholar]
  19. F. Hecht, New development in freefem++. J. Numer. Math. 20 (2012) 251–265. [Google Scholar]
  20. T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag, Berlin, Reprint of the corr. print. of the 2nd edition 1980 edition (1995). [CrossRef] [Google Scholar]
  21. S. Kim and J.E. Pasciak, Analysis of the spectrum of a Cartesian perfectly matched layer (PML) approximation to acoustic scattering problems. J. Math. Anal. Appl. 361 (2010) 420–430. [Google Scholar]
  22. V.A. Kozlov, V.G. Maz’ya and J. Rossmann, Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations. Vol. 85 of Mathematical Surveys and Monographs. AMS, Providence (2001). [Google Scholar]
  23. P. Kuchment, Graph models for waves in thin structures. Waves Random Media 12 (2002) R1. [CrossRef] [Google Scholar]
  24. P. Kuchment, Quantum graphs: an introduction and a brief survey, in Analysis on Graphs and its Applications. Selected papers based on the INI Programme, Cambridge, UK, January 8–June 29, 2007. American Mathematical Society (AMS), Providence, RI (2008) 291–312. [Google Scholar]
  25. P.A. Kuchment, Floquet theory for partial differential equations. Russ. Math. Surv. 37 (1982) 1. [CrossRef] [Google Scholar]
  26. P.A. Kuchment, Floquet Theory for Partial Differential Equations, Vol. 60. Springer Science & Business Media (1993). [CrossRef] [Google Scholar]
  27. P. Kuchment and H. Zeng, Asymptotics of spectra of Neumann laplacians in thin domains. Contemp. Math. 327 (2003) 199–214. [CrossRef] [Google Scholar]
  28. N. Moiseyev, Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling. Phys. Rep. 302 (1998) 212–293. [CrossRef] [Google Scholar]
  29. S. Molchanov and B. Vainberg, Scattering solutions in networks of thin fibers: small diameter asymptotics. Commun. Math. Phys. 273 (2007) 533–559. [CrossRef] [Google Scholar]
  30. S. Molchanov and B. Vainberg, Laplace operator in networks of thin fibers: spectrum near the threshold, in Stochastic Analysing in Mathematical Physics. Proceedings of a Satellite Conference of ICM 2006, Lisbon, Portugal, September 4–8, 2006. Selected papers. (2008) 69–94. [Google Scholar]
  31. S.A. Nazarov, Asymptotic analysis and modeling of the jointing of a massive body with thin rods. J. Math. Sci. 127 (2005) 2192–2262. [CrossRef] [MathSciNet] [Google Scholar]
  32. S.A. Nazarov, Properties of spectra of boundary value problems in cylindrical and quasicylindrical domains, in Sobolev Spaces in Mathematics II. Springer (2009) 261–309. [CrossRef] [Google Scholar]
  33. S.A. Nazarov, Trapped modes in a T-shaped waveguide. Acoust. Phys. 56 (2010) 1004–1015. [CrossRef] [Google Scholar]
  34. S.A. Nazarov, Discrete spectrum of cranked, branching, and periodic waveguides. St. Petersbg. Math. J. 23 (2012) 351–379. Transl. from Algebra i analiz 23 (2011) 206–247. [CrossRef] [Google Scholar]
  35. S.A. Nazarov, Asymptotics of eigenvalues of the Dirichlet problem in a skewed T-shaped waveguide. Zh. Vychisl. Mat. Mat. Fiz. 54 (2014) 793–814. [Google Scholar]
  36. S.A. Nazarov, Bounded solutions in a T-shaped waveguide and the spectral properties of the dirichlet ladder. Comput. Math. Math. Phys. 54 (2014) 1261–1279. [CrossRef] [MathSciNet] [Google Scholar]
  37. S.A. Nazarov, Discrete spectrum of cross-shaped quantum waveguides. J. Math. Sci. 196 (2014) 346–376. [CrossRef] [MathSciNet] [Google Scholar]
  38. S.A. Nazarov, Transmission conditions in one-dimensional model of a rectangular lattice of thin quantum waveguides. J. Math. Sci. 219 (2016) 994–1015. [CrossRef] [MathSciNet] [Google Scholar]
  39. S.A. Nazarov, The spectra of rectangular lattices of quantum waveguides. Izv. Math. 81 (2017) 29. [CrossRef] [MathSciNet] [Google Scholar]
  40. S.A. Nazarov, Breakdown of cycles and the possibility of opening spectral gaps in a square lattice of thin acoustic waveguides. Izv. Math. 82 (2018) 1148–1195. Transl. from Izv. Ross. Akad. Nauk Ser. Mat. 82 (2018) 78–127. [CrossRef] [MathSciNet] [Google Scholar]
  41. S.A. Nazarov, On the one-dimensional asymptotic models of thin Neumann lattices. Sib. Math. J. 64 (2023) 356–373. [CrossRef] [MathSciNet] [Google Scholar]
  42. S.A. Nazarov and B.A. Plamenevskiĭ, Elliptic Problems in Domains with Piecewise Smooth Boundaries. Vol. 13 of Expositions in Mathematics. De Gruyter, Berlin, Germany (1994). [Google Scholar]
  43. S.A. Nazarov, K. Ruotsalainen and P. Uusitalo, The Y-junction of quantum waveguides. Z. Angew Math. Mech. 94 (2014) 477–486. [CrossRef] [MathSciNet] [Google Scholar]
  44. S.A. Nazarov, K. Ruotsalainen and P. Uusitalo, Asymptotics of the spectrum of the Dirichlet Laplacian on a thin carbon nano-structure. C. R. Acad. Sci. Mec. 343 (2015) 360–364. [Google Scholar]
  45. K. Pankrashkin, Eigenvalue inequalities and absence of threshold resonances for waveguide junctions. J. Math. Anal. Appl. 449 (2017) 907–925. [CrossRef] [MathSciNet] [Google Scholar]
  46. L. Pauling, The diamagnetic anisotropy of aromatic molecules. J. Chem. Phys. 4 (1936) 673–677. [NASA ADS] [CrossRef] [Google Scholar]
  47. O. Post, Spectral Analysis on Graph-Like Spaces. Vol. 2039. Springer Science & Business Media (2012). [CrossRef] [Google Scholar]
  48. R.L. Schult, D.G. Ravenhall and H.W. Wyld, Quantum bound states in a classically unbound system of crossed wires. Phys. Rev. B 39 (1989) 5476. [CrossRef] [PubMed] [Google Scholar]
  49. B. Simon, Resonances and complex scaling: a rigorous overview. Int. J. Quantum Chem. XIV (1978) 529–542. [CrossRef] [Google Scholar]
  50. M.M. Skriganov, Geometric and Arithmetic Methods in the Spectral Theory of Multidimensional Periodic Operators. Vol. 171. American Mathematical Society (1987). [Google Scholar]

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