JournalsaihpcVol. 26, No. 5pp. 1743–1765

Lyapunov control of a quantum particle in a decaying potential

  • Mazyar Mirrahimi

    INRIA Rocquencourt, B.P. 105, Domaine de Voluceau, 78153 Le Chesnay Cedex, France
Lyapunov control of a quantum particle in a decaying potential cover
Download PDF

Abstract

A Lyapunov-based approach for the trajectory generation of an N-dimensional Schrödinger equation in whole RN\mathbb{R}^{N} is proposed. For the case of a quantum particle in an N-dimensional decaying potential the convergence is precisely analyzed. The free system admitting a mixed spectrum, the dispersion through the absolutely continuous part is the main obstacle to ensure such a stabilization result. Whenever, the system is completely initialized in the discrete part of the spectrum, a Lyapunov strategy encoding both the distance with respect to the target state and the penalization of the passage through the continuous part of the spectrum, ensures the approximate stabilization.

Cite this article

Mazyar Mirrahimi, Lyapunov control of a quantum particle in a decaying potential. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 5, pp. 1743–1765

DOI 10.1016/J.ANIHPC.2008.09.006