Controllability of the discrete-spectrum Schrödinger equation driven by an external field
By Thomas Chambrion, Paolo Mason, Mario Sigalotti, Ugo V. Boscain. 2008
174 citations recorded by the source corpus.
We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials.
Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a37bcd90bccbc888f616acfbf9efd068432f76d9
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In Computer Networks and Communications
In Mathematical Physics
In Statistical and Nonlinear Physics
- Dominique Sugny
- Christiane P. Koch
- Thomas Schulte-Herbrüggen
- Mikhail Lemeshko
- Ronnie Kosloff
- Tommaso Calarco
- Frank K. Wilhelm
- Steffen J. Glaser
Citations in the corpus
- Quantum control of molecular rotation (2018, methodology): “Approximate controllability is much more common and many different results have been obtained using, e.g., Galerkin techniques, i.e., finitedimensional approximations of the Hilbert space (Chambrion et al., 2009; Boscain et al., 2012, 2015; Boscain, Caponigro, and Sigalotti, 2014).”
- Local controllability of 1D linear and nonlinear Schr (2010, unknown): “In [30], by Boscain, Chambrion, Mason and Sigalotti, the authors prove the approximate controllability in L(2), for bilinear Schrödinger equations such as (1).”
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, methodology): “employ recurrence arguments similar to the finite-dimensional case [81, 82, 131, 326].”