On the controllability of quantum-mechanical systems

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

Research output: Contribution to journalArticle

290 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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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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