Magnetic Dirichlet Laplacian in curved waveguides

• Autorzy: Barseghyan Diana , Bernstein Swanhild , Schneider Baruch , Zimmermann Martha Lina

Identyfikatory

DOI

10.7494/OpMath.2025.45.3.293

• Języki publikacji: EN

Abstrakty

EN

For a two-dimensional curved waveguide, it is well known that the spectrum of the Dirichlet Laplacian is unstable with respect to waveguide deformations. This means that if the waveguide is a straight strip then the spectrum of the Dirichlet Laplacian is purely essential. From the other hand, the perturbation of the straight strip produces eigenvalues below the essential spectrum. In this paper, the Dirichlet–Laplace operator with a magnetic field is considered. We explicitly prove that the spectrum of the magnetic Laplacian is stable under small but non-local deformations of the waveguide.

Słowa kluczowe

EN

magnetic Schrödinger operators; essential spectrum; discrete spectrum

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2025
• Tom: Vol. 45, no. 3
• Strony: 293--305
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Barseghyan Diana

• University of Ostrava, Department of Mathematics, 30. dubna 22, 70103 Ostrava, Czech Republic

• https://orcid.org/0000-0003-0761-1157

autor

Bernstein Swanhild

• Technische Universität Bergakademie Freiberg, Institute of Applied Analysis, Akademiestrasse 6, Freiberg 09599, Germany

• https://orcid.org/0000-0002-8603-6682

autor

Schneider Baruch

• University of Ostrava, Department of Mathematics, 30. dubna 22, 70103 Ostrava, Czech Republic

• https://orcid.org/0000-0003-2933-3899

autor

Zimmermann Martha Lina

• Technische Universität Bergakademie Freiberg, Institute of Applied Analysis, Akademiestrasse 6, Freiberg 09599, Germany

• https://orcid.org/0000-0003-0030-1025

Bibliografia

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• [3] J. Bory-Reyes, D. Barseghyan, B. Schneider, Magnetic Schrödinger operator with the potential supported in a curved two-dimensional strip, Mediterr. J. Math. 21 (2024), 1–15.
• [4] W. Bulla, F. Gesztesy, W. Renger, B. Simon, Weakly coupled bound states in quantum waveguides, Proc. Amer. Math. Soc. 125 (1997), no. 5, 1487–1495.
• [5] P. Duclos, P. Exner, Curvature-induced bound states in quantum waveguides in two and three dimensions, Rev. Math. Phys. 7 (1995), 73–102.
• [6] T. Ekholm, H. Kovařík, Stability of the magnetic Schrödinger operator in a waveguide, Comm. Partial Differential Equations 30 (2005), 539–565.
• [7] P. Exner, H. Kovařík, Quantum Waveguides, Springer International, Heidelberg, 2015.
• [8] P. Exner, P. Šeba, Bound states in curved quantum wavequides, J. Math. Phys. 30 (1989), 2574–2580.
• [9] J. Goldstone, R.L. Jaffe, Bound states in twisting tubes, Phys. Rev. B 45 (1992), 14100–14107.
• [10] T. Kato, Perturbation Theory for Linear Operators, Springer, Berlin–Heidelberg–New York, 1966.
• [11] M. Reed, B. Simon, Methods of Modern Mathematical Physics, I. Functional Analysis, Academic Press, New York, 1980.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)