Voir la notice de l'article provenant de la source Math-Net.Ru
@article{CHFMJ_2024_9_4_a12, author = {A. G. Belolipetskaia and I. Yu. Popov}, title = {Influence of quantum graph parameters on the asymptotics of the number of resonances}, journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal}, pages = {682--688}, publisher = {mathdoc}, volume = {9}, number = {4}, year = {2024}, language = {en}, url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a12/} }
TY - JOUR AU - A. G. Belolipetskaia AU - I. Yu. Popov TI - Influence of quantum graph parameters on the asymptotics of the number of resonances JO - Čelâbinskij fiziko-matematičeskij žurnal PY - 2024 SP - 682 EP - 688 VL - 9 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a12/ LA - en ID - CHFMJ_2024_9_4_a12 ER -
%0 Journal Article %A A. G. Belolipetskaia %A I. Yu. Popov %T Influence of quantum graph parameters on the asymptotics of the number of resonances %J Čelâbinskij fiziko-matematičeskij žurnal %D 2024 %P 682-688 %V 9 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a12/ %G en %F CHFMJ_2024_9_4_a12
A. G. Belolipetskaia; I. Yu. Popov. Influence of quantum graph parameters on the asymptotics of the number of resonances. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 4, pp. 682-688. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_4_a12/
[1] Exner P., et al., Analysis on Graphs and Its Applications, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 2008
[2] Berkolaiko G., Kuchment P., Introduction to Quantum Graphs, American Mathematical Society, Providence, 2012
[3] Lax P.D., Phillips R.S., Scattering theory, Academic Press, New York, 1967
[4] Sjostrand J., Zworski M., “Complex scaling and the distribution of scattering poles”, Journal of American Mathematical Society, 4:4 (1991), 729–769
[5] Rouleux M., “Resonances for a semi-classical Schrödinger operator near a non trapping energy level”, Publ. RIMS, 34 (1998), 487–523, Kyoto University
[6] Exner P., Lotoreichik V., Tater M., “On resonances and bound states of Smilansky Hamiltonian”, Nanosystems: Physics, Chemistry, Mathematics, 7 (2016), 789–802
[7] Bonnet-Ben Dhia A.-S., Chesnel L., Pagneux V., “Trapped modes and reflectionless modes as eigenfunctions of the same spectral problem”, Proceedings of the Royal Society A, 474:2213 (2018)
[8] Khrushchev S.V., Nikol'skii N.K., Pavlov B.S., Unconditional bases of exponentials and of reproducing kernels, Springer-Verlag, Berlin, New York, 1981, 214–335 pp.
[9] Gadylshin R.R., “Existence and asymptotics of poles with small imaginary part for the Helmholtz resonator”, Russian Mathematical Surveys, 52:1 (1997), 1–72
[10] Blinova I.V., Popov A.I., Bosova A.A., “Spectral gaps for star-like quantum graph and for two coupled rings”, Nanosystems: Physics, Chemistry, Mathematics, 13:3 (2022), 425–429
[11] Popov I.Y., Yurova T.S., “Resonances for a solvable model of ultrasound scattering by a cell membrane”, JETP Letters, 118:2 (2023), 146–151
[12] Popov I., Yurova T.S., “Resonances for Laplacian perturbed on surface and cell membrane model”, Boletin de la Sociedad Matematica Mexicana, 29:3 (2023), 85
[13] Trifanova E.S., Bagmutov A.S., Katasonov V.G., Popov I.Y., “Asymptotic expansions of resonances for waveguides coupled through converging windows”, Chelyabinsk Physical and Mathematical Journal, 8:1 (2023), 72–82
[14] Davies E.B., Pushnitski A., “Non-Weyl resonance asymptotics for quantum graphs”, Analysis and PDE, 4 (2011), 729–756
[15] Davies E.B., Exner P., Lipovsky J., “Non-Weyl asymptotics for quantum graphs with general coupling conditions”, Journal of Physics A: Mathematical and Theoretical, 43 (2010), 474013
[16] Exner P., Lipovsky J., “Resonances from perturbations of quantum graphs with rationally related edges”, Journal of Physics A: Mathematical and Theoretical, 43:10 (2010), 105301
[17] Exner P., Lipovsky J., “Non-Weyl resonance asymptotics for quantum graphs in a magnetic field”, Physics Letters A, 375 (2011), 805–807
[18] Belolipetskaia A. G., Popov I.Y., “Dirac operator with different potentials on edges of quantum graph: resonance asymptotics”, Nanosystems: Physics, Chemistry, Mathematics, 12:4 (2021), 425–429
[19] Popov I.Y., Popov A.I., “Quantum dot with attached wires: Resonant states completeness”, Reports on Mathematical Physics, 80:1 (2017), 1–10
[20] Blinova I.V., Popov I.Y., “Quantum graph with the Dirac operator and resonance states completeness”, Operator Theory: Advances and Applications, 268 (2018), 111–124
[21] Gerasimov D.A., Popov I.Y., “Completeness of resonance states for quantum graph with two semi-infinite edges”, Complex Variables and Elliptic Equations, 63:7–8 (2018), 996–1010
[22] Blinova I.V., Popov I.Y., Popov A.I., “Resonance states completeness for relativistic particle on a sphere with two semi-infinite lines attached”, Journal of King Saud University — Science, 32:1 (2019), 836–841
[23] Popov I., Gerasimov D., Blinova I., Popov A., “Incompleteness of resonance states for quantum ring with two semi-infinite edges”, Analysis and Mathematical Physics, 9:3 (2019), 1287–1302