دورية أكاديمية
Local inverse scattering at a fixed energy for radial Schrödinger operators and localization of the Regge poles
| العنوان: | Local inverse scattering at a fixed energy for radial Schrödinger operators and localization of the Regge poles |
|---|---|
| المؤلفون: | Daudé, Thierry, Nicoleau, Francois |
| المساهمون: | Analyse, Géométrie et Modélisation (AGM - UMR 8088), Centre National de la Recherche Scientifique (CNRS)-CY Cergy Paris Université (CY), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), ANR-12-BS01-0012,AARG,Analyse Asymptotique en Relativité Générale(2012), ANR-11-BS01-0019,NOSEVOL,Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution(2011), ANR-13-JS01-0006,iproblems,Problèmes Inverses(2013) |
| المصدر: | ISSN: 1424-0637. |
| بيانات النشر: | HAL CCSD Springer Verlag |
| سنة النشر: | 2016 |
| المجموعة: | Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
| مصطلحات موضوعية: | radial Schrödinger operators, Inverse scattering, phase shifts, Regge poles, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
| الوصف: | 52 pages ; International audience ; We study inverse scattering problems at a fixed energy for radial Schr\"{o}dinger operators on $\R^n$, $n \geq 2$. First, we consider the class $\mathcal{A}$ of potentials $q(r)$ which can be extended analytically in $\Re z \geq 0$ such that $\mid q(z)\mid \leq C \ (1+ \mid z \mid )^{-\rho}$, $\rho > \frac{3}{2}$. If $q$ and $\tilde{q}$ are two such potentials and if the corresponding phase shifts $\delta_l$ and $\tilde{\delta}_l$ are super-exponentially close, then $q=\tilde{q}$. Secondly,we study the class of potentials $q(r)$ which can be split into $q(r)=q_1(r) + q_2(r)$ such that $q_1(r)$ has compact support and $q_2 (r) \in \mathcal{A}$.If $q$ and $\tilde{q}$ are two such potentials, we show that for any fixed $a>0$,${\ds{\delta_l - \tilde{\delta}_l \ = \ o \left( \frac{1}{l^{n-3}} \ \left( {\frac{ae}{2l}}\right)^{2l}\right)}}$ when $l \rightarrow +\infty$ if and only if $q(r)=\tilde{q}(r)$ for almost all $r \geq a$. The proofs are close in spirit with the celebrated Borg-Marchenko uniqueness theorem, and rely heavily on the localization of the Regge poles that could be defined as the resonances in the complexified angular momentum plane. We show that for a non-zero super-exponentially decreasing potential, the number of Regge poles is always infinite and moreover, the Regge poles are not contained in any vertical strip in the right-half plane. For potentials with compact support, we are able to give explicitly their asymptotics. At last, for potentials which can be extended analytically in $\Re z \geq 0$ with $\mid q(z)\mid \leq C \ (1+ \mid z \mid )^{-\rho}$, $\rho >1$ , we show that the Regge poles are confined in a vertical strip in the complex plane. |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| العلاقة: | info:eu-repo/semantics/altIdentifier/arxiv/1502.02276; hal-01114204; https://hal.archives-ouvertes.fr/hal-01114204Test; https://hal.archives-ouvertes.fr/hal-01114204v2/documentTest; https://hal.archives-ouvertes.fr/hal-01114204v2/file/radial12-06-2015.pdfTest; ARXIV: 1502.02276 |
| الإتاحة: | https://hal.archives-ouvertes.fr/hal-01114204Test https://hal.archives-ouvertes.fr/hal-01114204v2/documentTest https://hal.archives-ouvertes.fr/hal-01114204v2/file/radial12-06-2015.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.2FDBF4A8 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |