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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.
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 switc
We consider systems of weakly coupled Schrodinger equations with nonconstant potentials and we investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary c
This paper provides a brief introduction to learning control of quantum systems. In particular, the following aspects are outlined, including gradient-based learning for optimal control of quantum systems, evolutionary computation for learning contro
For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite
We consider general linear non-degenerate weakly-coupled cooperative elliptic systems and study certain monotonicity properties of the generalized principal eigenvalue in $mathbb{R}^d$ with respect to the potential. It is shown that monotonicity on t