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In control theory, understanding the observability property of a system is crucial for effectively managing and controlling dynamical systems. This property empowers us to deduce the internal state of a system from its outputs over time,…

It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…

We analyze the dynamical-algebraic approach to universal quantum control introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space $\cal H$ encoding information decomposes into irreducible sectors and subsystems…

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…

In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical…

We present a scheme for controlling the state of a quantum system by modifying the boundary conditions. This constitutes an infinite-dimensional control problem. We provide conditions for the existence of solutions of the dynamics and prove…

We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…

Quaternionic quantum Hamiltonians describing nonrelativistic spin particles require the ambient physical space to have five dimensions. The quantum dynamics of a spin-1/2 particle system characterised by a generic such Hamiltonian is worked…

This project investigates the approximate controllability of a class of stochastic integrodifferential equations in Hilbert space with non-local beginning conditions. In a departure from the conventional concerns expressed in the…

Control is a fundamental concept in quantum and reversible computational models. It enables the conditional application of a transformation to a system, depending on the state of another system. We introduce a general framework for…

We introduce a nonlocal control condition and the notion of approximate controllability for fractional order quasilinear control inclusions. Approximate controllability of a fractional control nonlocal delay quasilinear functional…

Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…

Many physical, chemical and biological systems can be modeled by means of random-frequency harmonic oscillator systems. Even though the noise-free evolution of harmonic oscillator systems can be easily implemented, the way to experimentally…

In this paper, we present a controllability analysis of the quantum Ising periodic chain of n spin 1/2 particles where the interpolating parameter between the two Hamiltonians plays the role of the control. A fundamental result in the…

Symmetric spaces arise in wide variety of problems in Mathematics and Physics. They are mostly studied in Representation theory, Harmonic analysis and Differential geometry. As many physical systems have symmetric spaces as their…

Dynamical systems can be coupled in a manner that is designed to drive the resulting dynamics onto a specified lower dimensional submanifold in the phase space of the combined system. On the submanifold, the variables of the two systems…

In this paper, we study some controllability and observability problems for stochastic systems coupling fourth- and second-order parabolic equations. The main goal is to control both equations with only one controller localized on the drift…

Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…

In this article, we give a condition for the global controllability of affine nonlinear control systems with drifts on Euclidean spaces. Under regularity assumptions, the condition is necessary and sufficient in the codimension-1 and…

The ability to manipulate coherently individual quantum objects organized in arrays is a prerequisite to any scalable quantum information platform. For electron spin qubits, it requires the fine tuning of large arrays of tunnel-coupled…