Out of equilibrium, disordered, and strongly interacting quantum and classical many body systems

包含大量相互作用的经典或量子粒子的系统的行为可能与单个组成粒子的行为截然不同。 正如诺贝尔奖获得者P.W.安德森，“越多越不一样”。 我将研究在三类物理系统中大量粒子相互作用产生的集体效应：无序的，强相关的电子材料;超冷原子气体和捕获的离子;和玻璃形成者。许多技术上有前途的材料，如高温超导体、磁性半导体和巨磁阻锰氧化物，其有用的性质来自于电子之间的强相关性及其与结构中固有缺陷（无序）的相互作用。我将开发理论方法，这将导致这些材料的电子状态的新见解。 超冷原子气体是有史以来最冷的物质，其温度高于绝对零度，并且人们对使用这些系统或捕获的离子作为操纵量子信息和创建量子计算机的平台的可能性感到非常兴奋。 在真实的时间中操纵这些系统的能力导致了我将从理论上研究的观察出平衡和耗散效应的可能性。 玻璃化提出了一个复杂的理论问题，因为它涉及到非常大量的微观单位的合作松弛。有一个越来越多的共识，玻璃系统中的原子或分子的局部排列在其宏观行为中起着关键作用，但这种关系还没有得到很好的理解-我将开发的理论方法，可以阐明微观粒子运动和宏观弛豫之间的联系。这些项目的结果将为这些系统提供新的见解和理论方法，并将为未来可能的研究途径提供指示，为加拿大在这些领域的强大研究社区做出贡献，特别是在强相关电子系统和冷原子和捕获离子方面。

The behaviour of systems containing large numbers of interacting classical or quantum particles can be dramatically different from the behaviour of individual constituent particles. As succinctly summarised by Nobel Laureate P.W. Anderson, "More is different". I will investigate collective effects that arise from the interactions of large numbers of particles in three classes of physical system: disordered, strongly correlated electron materials; ultra-cold atomic gases and trapped ions; and glass formers. Many technologically promising materials, such as high temperature superconductors, magnetic semiconductors, and colossal magnetoresistance manganites derive their useful properties from the strong correlations between electrons and its interplay with intrinsic imperfections, disorder, in their structure. I will develop theoretical approaches that will lead to new insights into electronic states of these materials. Ultra-cold atomic gases are the coldest matter ever realised, with temperatures of nanokelvins above absolute zero, and there has been much excitement about the possibility of using these systems, or trapped ions, as a platform for manipulating quantum information and creating a quantum computer. The ability to manipulate these systems in real time leads to the possibility of observing out of equilibrium and dissipative effects that I will study theoretically. Glassiness presents a complex theoretical problem, as it involves the co-operative relaxation of very large numbers of microscopic units. There is a growing consensus that local arrangements of atoms or molecules in glassy systems play a pivotal role in their macroscopic behaviour, but this relationship is not well understood -- I will develop theoretical approaches that can shed light on the connections between microscopic particle motion and macroscopic relaxations. The results from these projects will provide new insights and theoretical approaches to these systems and will give indications about possible future avenues for research, contributing to the strong Canadian research communities in these areas, especially in strongly correlated electron systems and cold atoms and trapped ions.