Related papers: On the problem of quantum control in infinite dime…
We consider the 1D nonlinear Schr\"odinger equation with bilinear control. In the case of Neumann boundary conditions, local exact controllability of this equation near the ground state has been proved by Beauchard and Laurent in…
The bilinear control problem of the Schr\"odinger equation $i\frac{\partial}{\partial t}\psi(t)$ $=(A+u(t) B)\psi(t)$, where $u(t)$ is the control function, is investigated through topological irreducibility of the set…
We show the approximate rotational controllability of a polar linear molecule by means of three nonresonant linear polarized laser fields. The result is based on a general approximate controllability result for the bilinear Schr\"odinger…
We provide bounds on the error between dynamics of an infinite dimensional bilinear Schr\"odinger equation and of its finite dimensional Galerkin approximations. Standard averaging methods are used on the finite dimensional approximations…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation…
We consider a system of an arbitrary number of \textsc{1d} linear Schr\"odinger equations on a bounded interval with bilinear control. We prove global exact controllability in large time of these $N$ equations with a single control. This…
The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the…
We investigate accessibility and controllability of a quantum system S coupled to a quantum probe P, both described by two-dimensional Hilbert spaces, under the hypothesis that the external control affects only P. In this context…
We prove that the multidimensional Schr\"odinger equation is exactly controllable in infinite time near any point which is a finite linear combination of eigenfunctions of the Schr\"odinger operator. We prove that, generically with respect…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels…
Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…
This paper completely solves the controllability problems of two-dimensional multi-input discrete-time bilinear systems with and without drift. Necessary and sufficient conditions for controllability, which cover the existing results, are…
We investigate the controllability of an infinite-dimensional quantum system: a quantum particle confined on a Thick Quantum Graph, a generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension with…
In quantum systems theory one of the fundamental problems boils down to: given an initial state, which final states can be reached by the dynamic system in question. Here we consider infinite dimensional open quantum dynamical systems…
We consider a linear Schr\"odinger equation, on a bounded interval, with bilinear control, that represents a quantum particle in an electric field (the control). We prove the controllability of this system, in any positive time, locally…
A variety of physically relevant bilinear Schr\"odinger equations are known to be approximately controllable in large times. There are however examples which are approximately controllable in large times, but not in small times. This…
In this paper, we study the problem of controllability of Schr\"odinger equation. We prove that the system is exactly controllable in infinite time to any position. The proof is based on an inverse mapping theorem for multivalued functions.…
We study a system composed of a free quantum particle trapped in a box whose walls can change their position. We prove the global approximate controllability of the system. That is, any initial state can be driven arbitrarily close to any…