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Register a new userWeakly-coupled systems in quantum control
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Added by
Nabile Boussaid
Publication date
2011
fields
Informatics Engineering
and research's language is
English
Authors
Nabile Boussaid
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This paper provides rigorous definitions and analysis of the dynamics of weakly-coupled systems and gives sufficient conditions for an infinite dimensional quantum control system to be weakly-coupled. As an illustration we provide examples chosen among common physical systems.
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In this article we study ergodic problems in the whole space $mathbb{R}^N$ for a weakly coupled systems of viscous Hamilton-Jacobi equations with coercive right-hand sides. The Hamiltonians are assumed to have a fairly general structure and the switching rates need not be constant. We prove the existence of a critical value $lambda^*$ such that the ergodic eigenvalue problem has a solution for every $lambdaleqlambda^*$ and no solution for $lambda>lambda^*$. Moreover, the existence and uniqueness of non-negative solutions corresponding to the value $lambda^*$ are also established. We also exhibit the implication of these results to the ergodic optimal control problems of controlled switching diffusions.
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