Alessandro Duca's Webpage

About me

I am an Associate Professor and Unlimited-term Researcher at Inria Nancy – Grand Est, affiliated with the Institute Élie Cartan de Lorraine. My research focuses on the control of quantum systems via time-dependent external fields and deformations of the confinement, with applications on standard domains and graph networks. I am particularly interested in exact and approximate controllability, energy permutation of quantum modes, and the development of explicit control strategies. Since October 2024, I have been coordinating the Nancy node of the ANR project QuBiCCS (project manager: Nabile Boussaid; project poles: Besançon and Nancy), collaborating with national and international teams on quantum control problems. I also work on controllability issues for parabolic equations, including linear and nonlinear heat equations and Burgers equations. From October 2025, I supervise the postdoctoral researcher Hugo Parada together with Rémi Buffe.

Professional background

From October 2025: Supervision of the postdoctoral researcher Hugo Parada together with Rémi Buffe.
From October 2024: Coordinator of the Nancy pole of the ANR project QuBiCCS (project manager: Nabile Boussaid; project poles : Besançon - Nancy).
From October 2022: Unlimited-term Researcher, Associate Professor, ISFP at Centre Inria Nancy - Grand Est (France).
February 2022 - October 2022: Tenure track Assistant professor ("Ricercatore di tipo B") at the University of Naples - Parthenope (Italy).
October 2020 - February 2022: Post-Doctoral position at the "Laboratoire de Mathématique de Versailles" financed by "Fondation Mathématiques Jacques Hadamard" (Supervised by Vahagn Nersesyan).
September 2018 - September 2020: Post-Doctoral position at the Institut Fourier financed by ANR ISDEEC: Interaction entre Systèmes Dynamiques, Equations d'Evolution et Contrôle (Supervised by Romain Joly).
2014 - 2018: PhD student in mathematics in the institutions "Università degli studi di Torino" (Italy), "Politecnico di Torino" (Italy) and "Université de Bourgogne Franche-Comté" (France) (supervised by Nabile Boussaid, Thomas Chambrion and Riccardo Adami).

Main publications

A. Duca, R. Joly, D. Turaev. Control of the Schrödinger equation by slow deformations of the domain. Annales de l'Institut Henri Poincaré, Analyse non linéaire, 2024. DOI, PDF.
A. Duca, V. Nersesyan. Bilinear control and growth of Sobolev norms for the nonlinear Schrödinger equation. Journal of the European Mathematical Society, 2025. DOI, PDF.
A. Duca, E. Pozzoli, C. Urbani. On the small-time bilinear control of a nonlinear heat equation: global approximate controllability and exact controllability to trajectories, Journal de Mathématiques Pures et Appliquées (in press), 2025. DOI,PDF.

Other publications

M. Abdelli, A. Ben Aissa, A. Duca, Well-posedness and exponential decay for the Euler-Bernoulli beam conveying fluid with non-constant velocity and dynamical boundary conditions. Zeitschrift fuer Angewandte Mathematik und Physik, 2021. DOI, PDF.
K. Ammari, A. Duca. Controllability of localized quantum states on infinite graphs through bilinear control fields. International Journal of Control, 2021. DOI, PDF.
K. Ammari, A. Duca. Controllability of periodic bilinear quantum systems on infinite graphs. Journal of Mathematical Physics, 2020.DOI, PDF.
K. Ammari, E. Bonnetier, A. Duca. Networks of sign-changing metamaterials: existence and spectral properties, Communications in Mathematical Sciences, 2025 (in press). PDF.
P. Cannarsa, A. Duca, C. Urbani. Exact controllability to eigensolutions of the bilinear heat equation on compact networks. Discrete Contin. Dyn. Syst. - S, 2022. DOI, PDF.
C. Castro, A. Duca. Achieving energy permutation of modes in the Schrödinger equation with moving Dirac potentials. Mathematical Control and Related Fields, 2024. PDF.
A. Duca. Bilinear quantum systems on compact graphs: well-posedness and global exact controllability. Automatica J. IFAC, 2021. DOI, PDF.
A. Duca. Controllability of bilinear quantum systems in explicit times via explicit control fields. International Journal of Control, 2021. DOI, PDF.
A. Duca. Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability. SIAM Journal on Control and Optimization, 2020. DOI, PDF.
A. Duca. Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations. Dynamics of Partial Differential Equations, 2020. DOI, PDF.
A. Duca, R. Joly. Schrödinger equation in moving domains. Annales Henri Poincaré, 2021. DOI, PDF.
A. Duca, R. Joly, D. Turaev. Permuting quantum eigenmodes by a quasi-adiabatic motion of the potential wall. Journal of Mathematical Physics, 2020. DOI, PDF.
A. Duca, V. Nersesyan. Local exact controllability of the 1D nonlinear Schrödinger equation in the case of Dirichlet boundary conditions, SIAM Journal on Control and Optimization, 2025. DOI, PDF.
A. Duca, E. Pozzoli. Small-time controllability for the nonlinear Schrödinger equation on $\mathbb{R}^N$ via bilinear electromagnetic fields, SIAM Journal on Control and Optimization, 2025. DOI, PDF.

Preprints

K. Ammari, A. Duca, R. Joly, K. Le Balc'h. The Graph Geometric Control Condition, 2025. PDF.
N. Boussaïd, A. Duca. $H^1$ local exact controllability of some one-dimensional bilinear Schrödinger equations, 2025. PDF.
R. Buffe, A. Duca. Exact controllability to eigensolutions of the fractional heat equation via bilinear controls on N-dimensional domains, 2025. PDF.
C. Castro, A. Duca. Energy permutation of quantum modes on a moving rectangular confinement: practical implementations and numerical evidences, 2025. PDF.
A. Duca, T. Takahashi. Small-time global controllability of the Burgers equation via bilinear controls, 2025. PDF.

Recent organized events

Workshop: "Quantum Lo : contrôle quantique en Lorraine", Institut Élie Cartan de Lorraine, Nancy, France, March 17-18, 2025 (Organized with Killian Lutz and Yannick Privat).
Workshop: "New Trends in Quantum Control", Université Côte d'Azur, Nice, France, October 16–17, 2024 (Organized with Ivan Beschastnyi and Eugenio Pozzoli).

Invited speaker to talks in conferences, workshops and schools

"Joint IFAC Conference (SSSC)-(TDS)-(COSY)", June-July 2025, Gif-sur-Yvette (France).
"Contrôle et Stabilisation des EDPs'', December 2024, Monastir (Tunisia).
Journées ANR QuBiCCS, October 2024, Besançon (France).
Control Theory & Inverse Problems (CTIP 2024), May 2024, Monastir (Tunisia).
JEDP de l'IECL, March 2024, Université de Lorraine, Nancy (France).
10 ans de l'IECL, October 2023, Université de Lorraine, Nancy (France).
ICIAM Congress, Minisymposium: Interplay between controllability and qualitative aspects of stochastic dynamical systems, August 2023, Waseda University, Tokyo (Japan).
Journées QUACO, June 2023, Laboratory Jacques-Louis Lions, Paris (France).
Journée scientifique Matière, systèmes et dispositifs quantique, June 2023, Université de Lorraine, Nancy (France).
Winter School on Control, stability and Singularities formation in Nonlinear PDE's, December 2022, Hammamet (Tunisia).
Analysis and Control of (bi)linear PDEs, September 2022, Tor Vergata University of Rome (Italy).
Analysis, Control and Inverse Problems for Diffusive Systems with Application to Natural and Social Sciences, July 2022, University of Bari (Italy).
Journées Jeunes EDPistes, March 2022, Institut Camille Jordan, Lyon (France).
Controllability of PDEs in physics models and applied sciences, February 2020, Rome (Italy).
VIII Partial differential equations, optimal design and numerics, August 2019, Benasque (Spain).
Identification and Control: Some challenges, June 2019, Monastir (Tunisia).
GDR Dynqua Bordeaux, February 2019, Bordeaux (France).
Workshop on PDE's: Modelling & Theory, 2018, Monastir (Tunisia).
Journées Jeunes EDPistes, March 2018, Nancy (France), poster exposition.
Second School and Workshop: Mathematical Challenges in Quantum Mechanics, February 2018, Rome (Italy).
Colloque INFINITI IHP, November 2017, Paris (France), poster exposition.
EDP-Normandie, October 2017, Caen (France), poster exposition.
Mathematical Control Theory, June 2017, Porquerolles (France).
La journée DISQUO, December 2016, Inria Paris (France).
Réunion du GT EDP May 2016, l'école des Mines à Paris (France).

Invited speaker to seminars

May 2024, CRAN, Université de Lorraine, Nancy (France).
September 2023, New York University of Shanghai, Shanghai (China).
March 2023 (control group workshop), Institut Élie Cartan de Lorraine, Nancy (France).
February 2023 (control group workshop), Institut Élie Cartan de Lorraine, Nancy (France).
January 2023 (control group workshop), Institut Élie Cartan de Lorraine, Nancy (France).
January 2023, INRIA, Nancy (France).
April 2022, University of Hagen (Germany).
December 2021, research group ``Mathematics in Cairo'' (Egypt).
Novembre 2021, Institut Élie Cartan de Lorraine, Nancy (France).
October 2021, Laboratoire de Mathématiques de Toulouse (France).
Avril 2021, Laboratoire de Mathématiques de Versailles (France).
Avril 2021, Laboratoire de Mathématiques et leurs Applications de Valenciennes (France).
March 2021, Gran Sasso Science Institute (Italy).
January 2020, University of Monastir (Tunisia).
December 2019, Laboratoire de Mathématiques de Toulouse (France).
December 2019 (control group workshop), Laboratoire de Mathématiques de Toulouse (France).
May 2019, Université Savoie Mont Blanc, Chambery (France).
January 2019, University of Monastir (Tunisia).
December 2017, Institut Fourier of Grenoble (France).
November 2017, Institut Élie Cartan de Lorraine, Nancy (France).

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