Computer-assisted existence proofs for one-dimensional Schrödinger-poisson systems
Motivated by the three-dimensional time-dependent Schr¨odinger-Poisson system we prove the existence of non-trivial solutions of the one-dimensional stationary Schr¨odinger-Poisson system using computer-assisted methods. Starting from a numerical approximate solution, we compute a bound for its defe...
Elmentve itt :
| Szerzők: | |
|---|---|
| Testületi szerző: | |
| Dokumentumtípus: | Cikk |
| Megjelent: |
University of Szeged, Institute of Informatics
Szeged
2020
|
| Sorozat: | Acta cybernetica
24 No. 3 |
| Kulcsszavak: | Számítástechnika, Kibernetika |
| Tárgyszavak: | |
| doi: | 10.14232/actacyb.24.3.2020.6 |
| Online Access: | http://acta.bibl.u-szeged.hu/69282 |
| LEADER | 01936nab a2200253 i 4500 | ||
|---|---|---|---|
| 001 | acta69282 | ||
| 005 | 20220621095536.0 | ||
| 008 | 200730s2020 hu o 0|| eng d | ||
| 022 | |a 0324-721X | ||
| 024 | 7 | |a 10.14232/actacyb.24.3.2020.6 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Wunderlich Jonathan | |
| 245 | 1 | 0 | |a Computer-assisted existence proofs for one-dimensional Schrödinger-poisson systems |h [elektronikus dokumentum] / |c Wunderlich Jonathan |
| 260 | |a University of Szeged, Institute of Informatics |b Szeged |c 2020 | ||
| 300 | |a 373-391 | ||
| 490 | 0 | |a Acta cybernetica |v 24 No. 3 | |
| 520 | 3 | |a Motivated by the three-dimensional time-dependent Schr¨odinger-Poisson system we prove the existence of non-trivial solutions of the one-dimensional stationary Schr¨odinger-Poisson system using computer-assisted methods. Starting from a numerical approximate solution, we compute a bound for its defect, and a norm bound for the inverse of the linearization at the approximate solution. For the latter, eigenvalue bounds play a crucial role, especially for the eigenvalues “close to” zero. Therefor, we use the Rayleigh-Ritz method and a corollary of the Temple-Lehmann Theorem to get enclosures of the crucial eigenvalues of the linearization below the essential spectrum. With these data in hand, we can use a fixed-point argument to obtain the desired existence of a non-trivial solution “nearby” the approximate one. In addition to the pure existence result, the used methods also provide an enclosure of the exact solution. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Számítás- és információtudomány | |
| 695 | |a Számítástechnika, Kibernetika | ||
| 700 | 0 | 1 | |a Plum Michael |e aut |
| 710 | |a Summer Workshop on Interval Methods (11.) (2018) (Rostock) | ||
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/69282/1/cybernetica_024_numb_003_373-391.pdf |z Dokumentum-elérés |