Effective quantum Hamiltonian in thin domains with non-homogeneity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00377970" target="_blank" >RIV/68407700:21340/25:00377970 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.57262/die038-0304-215" target="_blank" >https://doi.org/10.57262/die038-0304-215</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.57262/die038-0304-215" target="_blank" >10.57262/die038-0304-215</a>

Result language
angličtina
Original language name
Effective quantum Hamiltonian in thin domains with non-homogeneity
Original language description
We consider the Laplacian with a non-homogeneous metric in a tubular neighbourhood of a compact hypersurface in the Euclidean space of arbitrary dimension, subject to Neumann boundary conditions. It is shown that, in the limit of the width of the neighbourhood shrinking to zero, the operator converges in a generalised norm-resolvent sense to an effective Laplace-Beltrami-type operator on the hypersurface. In this way, we generalise and give an insight into the convergence of eigenvalues obtained by Yachimura (arXiv:1706.05027).
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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