On the controllability of quantum-mechanical systems

Garng Morton Huang, T. J. Tarn, John W. Clark

Research output: Contribution to journalArticle

288 Citations (Scopus)

Abstract

The systems-theoretic concept of controllability is elaborated for quantum-mechanical systems, sufficient conditions being sought under which the state vector ψ can be guided in time to a chosen point in the Hilbert space ℋ of the system. The Schrödinger equation for a quantum object influenced by adjustable external fields provides a state-evolution equation which is linear in ψ and linear in the external controls (thus a bilinear control system). For such systems the existence of a dense analytic domain script Dω in the sense of Nelson, together with the assumption that the Lie algebra associated with the system dynamics gives rise to a tangent space of constant finite dimension, permits the adaptation of the geometric approach developed for finite-dimensional bilinear and nonlinear control systems. Conditions are derived for global controllability on the intersection of script Dω with a suitably defined finite-dimensional submanifold of the unit sphere Sscript K in ℋ. Several soluble examples are presented to illuminate the general theoretical results.

Original languageEnglish
Pages (from-to)2608-2618
Number of pages11
JournalJournal of Mathematical Physics
Volume24
Issue number11
Publication statusPublished - 1 Dec 1982
Externally publishedYes

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controllability
Mechanical Systems
Controllability
Quantum Systems
Bilinear Systems
Nonlinear Control Systems
Tangent Space
state vectors
Geometric Approach
State Equation
Unit Sphere
Hilbert space
tangents
System Dynamics
Submanifolds
intersections
External Field
Evolution Equation
Lie Algebra
algebra

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

On the controllability of quantum-mechanical systems. / Huang, Garng Morton; Tarn, T. J.; Clark, John W.

In: Journal of Mathematical Physics, Vol. 24, No. 11, 01.12.1982, p. 2608-2618.

Research output: Contribution to journalArticle

Huang, GM, Tarn, TJ & Clark, JW 1982, 'On the controllability of quantum-mechanical systems', Journal of Mathematical Physics, vol. 24, no. 11, pp. 2608-2618.
Huang, Garng Morton ; Tarn, T. J. ; Clark, John W. / On the controllability of quantum-mechanical systems. In: Journal of Mathematical Physics. 1982 ; Vol. 24, No. 11. pp. 2608-2618.
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