Discrete spectrum of an asymmetric pair of waveguides coupled through a window

Sbornik Mathematics

Volumn 197, Issue 3-4, 2006, Pages 475-504

  Borisov, D I ^a,b  

^a BASHKIR STATE PEDAGOGICAL UNIVERSITY   (Russian Federation)

^b NUCLEAR PHYSICS INSTITUTE   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33747072086     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2006v197n04ABEH003767     Document Type: Article

References (24)

1. P. Exner, P. Seba, M. Tater, and D. Vaněk, "Bound states and scattering in quantum waveguides coupled laterally through a boundary window", J. Math. Phys. 37:10 (1996), 4867-4887.
2. Y. Hirayama, Y. Tokura, A. D. Wieck, S. Koch, R. J. Haug, K. von Klitzing, and K. Ploog, "Transport characteristics of a window-coupled in-plane-gated wire system", Phys. Rev. B 48:11 (1993), 7991-7998.
3. W. Bulla, F. Gesztesy, W. Renger, and B. Simon, "Weakly coupled bound states in quantum waveguides", Proc. Amer. Math. Soc. 125:5 (1997), 1487-1495.
4. P. Exner and S. Vugalter, "Asymptotics estimates for bound states in quantum waveguides coupled laterally through a narrow window", Ann. Inst. Henri Poincaré Phys. Théor. 65:1 (1996), 109-123.
5. P. Exner and S. Vugalter, "Bound-state asymptotic estimate for window-coupled Dirichlet strips and layers", J. Phys. A 30:22 (1997), 7863-7878.
6. I. Yu. Popov, "Asymptotics of bound states for laterally coupled waveguides", Rep. Math. Phys. 43:3 (1999), 427-437.
7. R. Gadyl'shin, "On regular and singular perturbation of acoustic and quantum waveguides", C. R. Mécanique 332:8 (2004), 647-652.
8. D. Borisov, P. Exner, and R. Gadyl'shin, "Geometric coupling thresholds in a two-dimensional strip", J. Math. Phys. 43:12 (2002), 6265-6278.
9. Ch. Kunze, "Leaky and mutually coupled wires", Phys. Rev. 048:19 (1993), 14338-14346.
10. J. Dittrich and J. Křiž, "Bound states in straight quantum waveguide with combined boundary condition", J. Math. Phys. 43:8 (2002), 3892-3915.
11. D. Borisov, T. Ekholm, and H. Kovařík, "Spectrum of the magnetic Schrödinger operator in a waveguide with combined boundary conditions", Ann. Inst. Henri Poincarê 6:2 (2005), 327-342.
12. M. Sh. Birman, "Perturbations of the continuous spectrum of a singular elliptic operator under perturbations of the boundary and the boundary conditions", Vestnik Leningrad. Univ. 17:1 (1962), 22-55. (Russian)
13. R. A. Adams, Sobolev spaces, Pure Appl. Math., vol. 65, Academic Press, New York 1975.
14. V. P. Mikhailov, Partial differential equations, Nauka, Moscow 1976; English transl., Mir, Moscow 1978.
15. M. Reed and B. Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press, New York 1978.
16. J. Blank, P. Exner, and M. Havliček, Hubert space operators in quantum physics, AIP Press, New York 1994.
17. T. Kato, Perturbation theory for linear operators, Springer-Verlag, New York 1966.
18. D. Borisov and P. Exner, "Exponential splitting of bound states in a waveguide with a pair of distant windows", J. Phys. A 37:10 (2004), 3411-3428.
19. E. Sánchez-Palencia, Nonhomogeneous media and vibration theory, Springer-Verlag, Berlin 1980.
20. R. R. Gadyl'shin, "Local perturbations of the Schrödinger operator on the axis", Teoret. Mat. Fiz. 132:1 (2002), 97-104;
21. English transl. in Theoret. and Math. Phys. 132 (2002), 976-982.
22. R. R. Gadyl'shin, "Local perturbations of the Schrödinger operator in the plane", Teoret. Mat. Fiz. 138:1 (2004), 41-54;
23. English transl. in Theoret. and Math. Phys. 138 (2004), 33-44.
24. A. M. Il'in, Matching of asymptotic expansions of solutions of boundary value problems, Nauka, Moscow 1989; English transl., Amer. Math. Soc., Providence, RI 1992.