Quantum Information Transport, Algebra Representations, Orthogonal Polynomials and (Super)Integrable Models

理论物理学试图通过提供各种现象的数学模型来理解自然。要确认这些描述并确定它们所涉及的预测，就需要对这些系统的动态有详细的了解。这就是“解决一个模型”的意思，如果能准确地做到这一点就更好了。因此，重要的是发展数学和工具，使越来越多的相关动力系统的精确解成为可能，并有助于设计丰富和复杂的物理模型。吕克·维奈的研究将恰恰做到这一点。他将设计与量子计算机相关的设备。他将与实验者合作，以验证他的理论预测。他将发展新的数学，以推动各种问题的精确解决方案，他将找到新的模型，其动力学可以被完全理解。*为了量子信息的运行，量子比特，即量子态，需要在位置之间有效地传输。一种称为量子纠缠的资源，EBITS，也必须是可用的。吕克·维内将探索如何使用被称为量子自旋链的物理系统来完成这些任务。*自旋链的动力学可以在由耦合波导阵列形成的光子晶格中重现。吕克·维内将与实验者合作，在根据他为此目的确定的自旋链的规格设计的阵列中实现量子比特的传输和EBIT的产生。*高度对称是允许精确解的系统的典型特征。作为这些问题的专家，吕克·维内将推进与该关键字相关的数学，这些关键字被称为代数和表示论。他将发现易于描述不变情况的新结构，还将确定通常被称为特殊的新函数，这些新函数通过它们的性质来编码对称。*吕克·维内也有策略来构造具有许多称为超可积的对称性的新模型，这些对称性是精确可解模型的标志。他将为他们的研究带来新的数学结果，并将探索他们的现象学和应用

Theoretical physics attempts to understand nature by offering mathematical models of various phenomena. The validation of those descriptions and the determination of the predictions they entail require a detailed understanding of the dynamics of those systems. This is what is meant by « solving a model » and the better if this can be done exactly. It is therefore important to develop the mathematics, the tools, that will make possible the exact solution of a growing number of relevant dynamical systems and will help in the design of rich and sophisticate physical models.******The research of Luc Vinet will do precisely that. He will design devices relevant for quantum computers. He will work with experimentalists to validate his theoretical predictions. He will develop new mathematics that will advance the exact solutions of various problems and he will find new models whose dynamics can be fully understood.******For quantum information to operate, qubits i.e. quantum states need to be transported efficiently between locations. A resource known as quantum entanglement, ebits, must also be available. Luc Vinet will explore how one can use physical systems known as quantum spin chains to achieve those tasks. ******The dynamics of spin chains can be reproduced in photonic lattices formed by arrays of coupled waveguides. Luc Vinet will work with experimentalists to implement the transport of qubits and the generation of ebits in arrays engineered according to the specifications of the spin chains he will have identified for that purpose.******A high level of symmetry is typically a feature of systems admitting an exact solution. An expert of those questions, Luc Vinet will advance the mathematics associated with that key word which are referred to as algebra and representation theory. He will find new structures apt to describe situations of invariance and will also identify new functions often called special that encode symmetries through their properties.******Luc Vinet also has strategies to construct new models with a lot of symmetries called superintegrable that are the hallmark of exactly solvable models. He will bring new mathematical results to bear on their study and will explore their phenomenology and applications