Regular propagators of bilinear quantum systems
| Autor: | Marco Caponigro, Nabile Boussaid, Thomas Chambrion |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique et numérique (M2N), Conservatoire National des Arts et Métiers [CNAM] (CNAM), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Projet CRNS Infiniti 'DISQUO', ANR-17-CE40-0007,QUACO,Contrôle quantique : systèmes d'EDPs et applications à l'IRM(2017), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM) |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
bilinear control Bilinear interpolation 01 natural sciences Schrödinger equation symbols.namesake Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics bounded variation [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics - Optimization and Control Contraction (operator theory) Quantum Mathematics Shrodinger equation 010102 general mathematics Hilbert space Propagator Quantum control Real-valued function Optimization and Control (math.OC) Settore MAT/05 Bounded variation symbols [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 010307 mathematical physics Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Functional Analysis Journal of Functional Analysis, Elsevier, 2020, 278 (6), pp.108412. ⟨10.1016/j.jfa.2019.108412⟩ Journal of Functional Analysis, 2020, 278 (6), pp.108412. ⟨10.1016/j.jfa.2019.108412⟩ |
| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1016/j.jfa.2019.108412 |
| Popis: | The present analysis deals with the regularity of solutions of bilinear control systems of the type $x'=(A+u(t)B)x$ where the state $x$ belongs to some complex infinite dimensional Hilbert space, the (possibly unbounded) linear operators $A$ and $B$ are skew-adjoint and the control $u$ is a real valued function. Such systems arise, for instance, in quantum control with the bilinear Schr\"{o}dinger equation. For the sake of the regularity analysis, we consider a more general framework where $A$ and $B$ are generators of contraction semi-groups. Under some hypotheses on the commutator of the operators $A$ and $B$, it is possible to extend the definition of solution for controls in the set of Radon measures to obtain precise a priori energy estimates on the solutions, leading to a natural extension of the celebrated noncontrollability result of Ball, Marsden, and Slemrod in 1982. Complementary material to this analysis can be found in [hal-01537743v1] |
| Databáze: | OpenAIRE |
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