Ph. Briet, H. Kovarik, G. Raikov, E. Soccorsi, Eigenvalue asymptotics in a twisted waveguide, Commun. P.D.E. 34 (2009), 818 - 836.
Cited by:
D. Krejcırık, E. Zuazua, The Hardy inequality and the heat equation in twisted tubes, Journal de Mathématiques Pures et Appliquées 94 (2010), 277–303.
D. Borisov, G. Cardone, Planar waveguide with “twisted” boundary conditions: discrete spectrum, J. Math. Phys. 52 (2011), 123513, 24 pp.
C. de Oliveira, A. Verri, On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes, J. Math. Anal. Appl. 381 (2011), 454-468 .
C. de Oliveira, A. Verri, On norm resolvent and quadratic form convergences in asymptotic thin spatial waveguides, In: Spectral analysis of quantum Hamiltonians, 253-276, Oper. Theory Adv. Appl., 224 Birkhäuser/Springer Basel AG, Basel, 2012.
P. Exner, D. Barseghyan, Spectral estimates for Dirichlet Laplacians and Schrödinger operators on geometrically nontrivial cusps, J. Spectr. Theory 3 (2013), 465–484.
P. Exner, D. Barseghyan, Spectral estimates for Dirichlet Laplacians on perturbed twisted tubes, Operators and Matrices 8 (2014), 167-183.
V. Bruneau, N. Popoff, On the ground state energy of the Laplacian with a magnetic field created by a rectilinear current, J. Funct. Anal. 268 (2015), 1277-1307.
T. Lungenstrass, Spectral Properties of Magnetic Quantum Systems, Ph. D. Thesis, Pontificia Universidad Católica de Chile, Santiago de Chile, 2015.
V. Bruneau, K. Pankrashkin, N. Popoff, Eigenvalue counting function for Robin Laplacians on conical domains, J. Geom. Anal., 28 (2018), 123-151.
C. R. Mamani, Espectro absolutamente contínuo do operador Laplaciano, Tese de Doutorao, Universidade Federal de Sao Carlos, 2018.
V. Bruneau, P. Miranda, N. Popoff, Resonances near thresholds in slightly twisted waveguides, Proceedings AMS 146 (2018), 4801-4812.
C. R. Mamani, A. A. Verri, Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides, Bulletin of the Brazilian Mathematical Society, 49 (2018), 495-513.
C. R. Mamani, A. A. Verri, Influence of bounded states in the Neumann Laplacian in a thin waveguide, Rocky Mountain J. Math. 48 (2018), 1993–2021.
A.A.Verri, Dirichlet Laplacian in a thin twisted strip, International Journal of Mathematics, 30, n°2, 1950006 (2019).
N. Popoff, Magnetic fields and boundary conditions in spectral and asymptotic analysis, Mémoire d’Habilatation à Diriger les Recherches, Université de Bordeaux, 2019.
A. A. Verri, Dirichlet Laplacian in a thin twisted strip, Internat. J. Math. 30 (2019), 1950006.
D. Barseghyan, A. Khrabustovskyi, Spectral estimates for Dirichlet Laplacian on tubes with exploding twisting velocity, Oper. Matrices 13 (2019), 311–322.
V. Bruneau, P. Miranda, D. Parra, N. Popoff, Eigenvalue and Resonance Asymptotics in Perturbed Periodically Twisted Tubes: Twisting Versus Bending, Annales Henri Poincaré, 21 (2020), 377–403.
P. Exner, V. Lotoreichik, Spectral asymptotics of the Dirichlet Laplacian on a generalized parabolic layer, Integral Equations Operator Theory 92 (2020), Paper No. 15.
A.S. Bagmutov, I.Y. Popov, Window-coupled nanolayers: window shape influence on one-particle and two-particle eigenstates, Nanosystems: Physics, Chemistry, Mathematics, 11 (2020) n 6, 636–641.
Alessandra A. Verri, Spectrum of the Dirichlet Laplacian in waveguides with parallel cross-sections, Preprint arXiv:2005.04772 (2020).
Alessandra A. Verri, Spectrum of the Dirichlet Laplacian in sheared waveguides, Zeitschrift für angewandte Mathematik und Physik, 72 (2021), article number: 23, 12 pp. https://doi.org/10.1007/s00033-020-01444-z
A. S. Bagmutov, H. Najar, I. F. Melikhov, I. Y. Popov, On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field, Nanosystems : Physics, Chemistry, Mathematics; St. Petersburg 13 (2022), n. 2, 156-163.
David Krejcirik, Spectral geometry of tubes, Mini-courses in Mathematical Analysis 2023, Padova, 19–23 June 2023. hal-04159525. https://hal.science/hal-04159525 .
A.S.Bagmutov, Spectral analysis of systems with interactions on sets of measure zero (in Russian), Ph.D. thesis, ITMO University, St. Petersburg, Russia, 2023.
А.С.Багмутов, Спектральный анализ систем с взаимодействиями на множествах нулевой меры, Диссертация на соискание учёной степени кандидата физико-математических наук, Национальный Исследовательский Университет ИТМО, 2023.