Total Variation of the Control and Energy of Bilinear Quantum Systems
Nabile Boussaid (LM-Besan\c{c}on), Marco Caponigro (M2N), Thomas, Chambrion (IECL, INRIA Nancy - Grand Est / IECN / LMAM)
TL;DR
This paper investigates the relationship between control variation and energy change in bilinear quantum systems, providing examples and optimal estimates for systems with different coupling bounds.
Contribution
It offers new examples and optimal estimates linking control total variation to energy variation in bilinear quantum systems with bounded or unbounded coupling.
Findings
Good agreement between control variation and energy variation observed.
Estimates in terms of control variation are shown to be optimal.
Applicable to systems with both bounded and unbounded coupling terms.
Abstract
In the present note, we give two examples of bilinear quantum systems showing good agreement between the total variation of the control and the variation of the energy of solutions, with bounded or unbounded coupling term. The corresponding estimates in terms of the total variation of the control appear to be optimal.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Laser-Matter Interactions and Applications · Stability and Controllability of Differential Equations