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。这些描述的验证和它们所带来的预测的确定需要对这些系统的动力学有详细的了解。这就是“求解模型”的含义，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，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而复杂的物理模型。

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