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

理论物理试图通过提供各种现象的数学模型来理解自然。验证这些描述和确定它们所需的预测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，如果能精确地完成就更好了。因此，重要的是要发展数学，工具，这将使越来越多的相关动力系统的精确解成为可能，并将有助于设计丰富和可扩展的物理模型。吕克·维奈（Luc Vinet）的研究恰恰可以做到这一点。他将设计与量子计算机相关的设备。他将与实验学家合作，以验证他的理论预测。他将开发新的数学，将推进各种问题的精确解决方案，他将找到新的模型，其动力学可以完全理解。为了使量子信息运行，量子比特（即量子态）需要在位置之间有效地传输。一种被称为量子纠缠（ebits）的资源也必须可用。Luc Vinet将探索如何使用被称为量子自旋链的物理系统来实现这些任务。** 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再现。Luc Vinet将与实验人员合作，根据他为此目的确定的自旋链的规格，在设计的阵列中实现量子比特的传输和ebit的生成。高度对称性是系统的一个典型特征，它允许有精确解。作为这些问题的专家，Luc Vinet将推进与这个关键词相关的数学，这些关键词被称为代数和表示论。他将发现新的结构，易于描述不变性的情况，也将确定新的功能，通常被称为特殊的编码对称性，通过其属性。Luc Vinet也有策略来构建具有大量对称性的新模型，称为超可积模型，这是精确可解模型的标志。他将带来新的数学成果，承担他们的研究，并将探讨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