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

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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.