Abstract
We consider a Stark Hamiltonian on a two-dimensional bounded domain with Dirichlet boundary conditions. In the strong electric field limit we derive, under certain local convexity conditions, a three-term asymptotic expansion of the low-lying eigenvalues. This shows that the excitation frequencies are proportional to the square root of the boundary curvature at a certain point determined by the direction of the electric field.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | SIAM Journal on Mathematical Analysis |
| Vol/bind | 54 |
| Udgave nummer | 2 |
| Sider (fra-til) | 2114-2127 |
| Antal sider | 14 |
| ISSN | 0036-1410 |
| DOI | |
| Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:\ast Received by the editors December 17, 2020; accepted for publication (in revised form) December 28, 2021; published electronically April 11, 2022. https://doi.org/10.1137/20M1386712 Funding: The work of the second author was supported by the Czech Science Foundation (GACR) EXPRO grant 20-17749X and by Aalborg University for supporting his stay in 2019. The work of the fifth author was partially supported by the Fondecyt (Chile) project 118-0355. \dagger Department of Mathematical Sciences, Aalborg University, Skjernvej 4A, 9220 Aalborg, Denmark ([email protected]). \ddagger Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 12000 Prague 2, Czechia ([email protected]). \S Department of Materials and Production, Aalborg University, Skjernvej 4A, 9220 Aalborg, Denmark ([email protected]). \P Laboratoire Angevin de Recherche en Math\e'matiques, LAREMA, UMR 6093, UNIV Angers, SFR Math-STIC, 2 boulevard Lavoisier 49045 Angers Cedex 01, France ([email protected]). \| Instituto de F\{\'i}sica, Pontificia Universidad Cato\'lica de Chile, Vicun\~a Mackenna 4860, Santiago 7820436, Chile ([email protected]).
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© 2022 Society for Industrial and Applied Mathematics.