Local controllability of a 1-D Schrödinger equation

By Karine Beauchard. 2005

187 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/535a1b7df00dfb2f54737a58a538d54276aa3393

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In Applied Mathematics

In Control and Systems Engineering

In Statistical and Nonlinear Physics

Citations in the corpus

Training Schrödinger’s cat: quantum optimal control (2015, background): “erty to exact controllability [229, 157] recently completed by some positive results about exact [18, 19] or approximate controllability based on Galerkin techniques [47].”
Controllability of the discrete-spectrum Schrödinger equation driven by an external field (2008, background): “In [12, 13] Beauchard and Coron study the controllability of a quantum particle in a 1D potential well with W (x) = x.”
GLOBAL STEADY-STATE STABILIZATION AND CONTROLLABILITY OF 1D SEMILINEAR WAVE EQUATIONS (2006, methodology): “The method consisting in stabilizing a quasi-static deformation has already been used in [8] in the context of nonlinear heat equations, in [23] for Navier–Stokes equations, in [7] for shallow water equations, and in [3, 4] for a Schrödinger equation.”
Controllability of a quantum particle in a moving potential well (2006, methodology): “It has already been proved in [1] that the subsystem”
Quantum control of molecular rotation (2018, background): “In the case of an infinite-dimensional Hilbert space, the problem is much more intricate from a mathematical point of view, even for a quantum system with a discrete spectrum (Beauchard, 2005; Chambrion et al., 2009; Boscain et al., 2012, 2015; Boscain, Caponigro, and Sigalotti, 2014).”
Control of a Korteweg-de Vries equation: A tutorial (2013, methodology): “To address this problem and the previous one, a possible approach would be to prove the exact controllability of the nonlinear equation around nontrivial stationary solutions (as proved by Crépeau in [20, 21] in the case of homogeneous Dirichlet boundary conditions), and then to apply the method int”
Boundary controllability for the nonlinear Korteweg–de Vries equation on any critical domain (2009, methodology): “This method and others such as quasi-static deformations (see [1,12,13] and [10, Chapter 7]) and the return method (see [1,6–8] and [10, Chapter 6]) are very useful to deal with nonlinear systems and to get properties which are not a consequence of the linearized system behavior.”
Controllability and Observability of Partial Differential Equations: Some Results and Open Problems (2007, methodology): “Beauchard [8] (see also [9] for a global version of the same result and the references therein) where this problem is solved by a combination of several tools including Coron’s return method ([34]) and Nash-Moser’s iteration.”
On the controllability of the 1-D isentropic Euler equation (2007, methodology): “Coron in [14] in the context of finite-dimensional systems, and used since for various PDE problems such as Euler incompressible equation [15, 19], Burgers equation [24], Vlasov–Poisson equation [20], Schrödinger equation [6, 7].”
Local controllability of 1D linear and nonlinear Schr (2010, unknown): “Des résultats similaires ont déjá été établis (Beauchard, 2005, 2008, 2006) [14,15,17], mais dans des espaces non optimaux, en temps long et leur démonstration reposait sur le théorème de Nash–Moser, pour gérer une apparente perte de régularité.”