Search results for "Quantum physic"
showing 10 items of 1596 documents
On the determination of the intramolecular potential energy surface of polyatomic molecules: Hydrogen sulfide and formaldehyde as an illustration
2009
International audience; We present here an approach for determining the Hamiltonian of polyatomic molecules that allows one to successfully solve the problem of potential energy surface (PES) determination via construction and diagonalization of a Hamiltonian matrix of large dimension. In the suggested approach, the Hamiltonian is very simple and can be used both for any "normal" polyatomic molecule and for any isotopic species of a molecule. Molecules with two to four equivalent X-Y bonds are considered, and for illustration of the efficiency of the suggested approach, numerical calculations are made for the three-atomic (hydrogen sulfide) and four-atomic (formaldehyde) molecules.
Microstructure-oxidation resistance relationship in Ti3AlC2 MAX phase
2020
International audience; Spark Plasma Sintering and Hot Isostatic Pressing were used to synthesize coarse-grained and fine-grained Ti3AlC2 specimens. Moreover, Spark Plasma Sintering processing parameters were modified in order to vary the TiC, Al2O3 and TixAly impurity and the porosity contents in the fine-grained samples. The influence of the Ti3AlC2 microstructure on the oxidation resistance was assesed. It is demonstrated that the grain size can drastically modify the oxidation resistance. The higher density of grain boundaries, in fine-grained specimens, increases the number of Al diffusion paths and leads to the formation of a protective alumina scale. In coarse-grained sample, Al diff…
Notice of Violation of IEEE Publication Principles: Robust Observer Design for Unknown Inputs Takagi–Sugeno Models
2013
This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.
Introduction to the Pontryagin Maximum Principle for Quantum Optimal Control
2021
Optimal Control Theory is a powerful mathematical tool, which has known a rapid development since the 1950s, mainly for engineering applications. More recently, it has become a widely used method to improve process performance in quantum technologies by means of highly efficient control of quantum dynamics. This tutorial aims at providing an introduction to key concepts of optimal control theory which is accessible to physicists and engineers working in quantum control or in related fields. The different mathematical results are introduced intuitively, before being rigorously stated. This tutorial describes modern aspects of optimal control theory, with a particular focus on the Pontryagin …
External constraints on optimal control strategies in molecular orientation and photofragmentation: Role of zero-area fields
2013
We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodissociation.
Time optimization and state-dependent constraints in the quantum optimal control of molecular orientation
2014
We apply two recent generalizations of monotonically convergent optimization algorithms to the control of molecular orientation by laser fields. We show how to minimize the control duration by a step-wise optimization and maximize the field-free molecular orientation using state-dependent constraints. We discuss the physical relevance of the different results.
Design of robust observer for T-S fuzzy time-delayed systems subject to unknown inputs
2013
In this paper, a novel approach is proposed to design a robust observer for a class of Takagi-Sugeno (T-S) fuzzy models with unknown inputs and delays. The main contribution of this paper is to consider unknown inputs and a mixed neutral and discrete delay in the model. Also, the system is subject to disturbances, which are imposed on both state and output signals. Delay-dependent sufficient conditions for the design of an unknown input T-S observer with time delays are given in terms of linear matrix inequalities (LMIs). Some relaxations are introduced by using intermediate variables. A numerical example is given to illustrate the effectiveness of the given results.
Jordan Decompositions of Tensors
2022
We expand on an idea of Vinberg to take a tensor space and the natural Lie algebra which acts on it and embed them into an auxiliary algebra. Viewed as endomorphisms of this algebra we associate adjoint operators to tensors. We show that the group actions on the tensor space and on the adjoint operators are consistent, which endows the tensor with a Jordan decomposition. We utilize aspects of the Jordan decomposition to study orbit separation and classification in examples that are relevant for quantum information.
Finite-temperature geometric properties of the Kitaev honeycomb model
2018
We study finite temperature topological phase transitions of the Kitaev's spin honeycomb model in the vortex-free sector with the use of the recently introduced mean Uhlmann curvature. We employ an appropriate Fermionisation procedure to study the system as a two-band p-wave superconductor described by a BdG Hamiltonian. This allows to study relevant quantities such as Berry and mean Uhlmann curvatures in a simple setting. More specifically, we consider the spin honeycomb in the presence of an external magnetic field breaking time reversal symmetry. The introduction of such an external perturbation opens a gap in the phase of the system characterised by non-Abelian statistics, and makes the…
Biorthogonal vectors, sesquilinear forms, and some physical operators
2018
Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized Riesz systems, enjoying certain properties. In particular we discuss what happens when they forms two $\D$-quasi bases.