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。正如诺贝尔奖得主P·W·安德森(P.W.Anderson)简明扼要地总结的那样，“越多越不同”。我将研究三类物理系统中大量粒子相互作用所产生的集体效应：无序的、强关联的电子材料；超冷原子气体和囚禁离子；以及玻璃形成器。许多技术上有前途的材料，如高温超导体、磁性半导体和巨磁电阻锰氧化物，都是由于电子之间的强相关性及其与结构中固有的缺陷和无序的相互作用而产生的有用的性质。我将开发理论方法，从而对这些材料的电子状态有新的见解。超冷原子气体是人们认识到的最冷的物质，纳米开尔文的温度超过绝对零度，人们对使用这些系统或囚禁离子作为操纵量子信息和创造量子计算机的平台的可能性感到非常兴奋。实时操纵这些系统的能力导致了观察到失衡和耗散效应的可能性，我将从理论上研究这一点。玻璃性是一个复杂的理论问题，因为它涉及大量微观单位的协同松弛。越来越多的人达成共识，认为玻璃系统中原子或分子的局部排列在它们的宏观行为中起着关键作用，但这种关系还没有被很好地理解--我将开发出能够阐明微观粒子运动和宏观弛豫之间联系的理论方法。这些项目的结果将为这些系统提供新的见解和理论方法，并将指示未来可能的研究途径，有助于加拿大在这些领域的强大研究社区，特别是在强关联电子系统和冷原子和囚禁离子方面。

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.