Dynamics of Non-Equilibrium Systems and Theory of Quantum Fluids and Solids

研究的一部分是一个理论程序，以调查 非平衡系统空间结构与复杂动力学 在有限波数的不稳定性阈值附近。 在定常不稳定性方面已经取得了相当大的进展， 例如纯流体中的对流。 实验 二元流体混合物中的对流提供了 理论工作丰富的行为附近的阈值 动态不稳定性 所用的方法是微扰法 导致“振幅”和“相位”方程的方案;数值 全流体方程的解，以回答特定的 问题;以及简单模型的数值模拟 构造方程来捕捉附近的重要物理 不稳定性 虽然流体系统提供了方便的系统， 为了仔细比较理论和实验， 研究成果应广泛适用于不同领域。 另一部分工作将研究体相和界面相 氦，既要了解这些的微观行为， 简单但具有挑战性的量子系统模型，并研究 它们是新参数体系中新物理学的实验室， 其中量子效应支配着热效应和碰撞效应 松弛效应通常很小。 蒙特-卡罗方法提供了 是研究微观物理的重要工具， 必须与分析现象学联系起来，才能产生任何真实的 认识 界面氦提供了一个有趣的两个- 三维热力学系统，并具有显着的， 实验上重要的运输行为， 明白

Part of the study is a theoretical program to investigate the spatial structure and complex dynamics in non-equilibrium systems near the threshold of an instability at finite wavenumber. Considerable progress has been made for stationary instabilities, exemplified by convection in pure fluids. Experiments on convection in binary fluid mixtures provide the impetus for theoretical work on the rich behavior near the threshold of a dynamic instability. The methods to be used are perturbational schemes leading to "amplitude" and "phase" equations; numerical solution of the full fluid equations to answer specific questions; and the numerical simulation of simpler model equations constructed to capture the important physics near the instabilities. Although fluid systems provide convenient systems for a careful comparison between theory and experiment, the results should have wide applicability in diverse fields. The other part of the work will study bulk and interfacial Helium, both to understand the microscopic behavior of these simple but challenging model quantum systems, and to investigate them as laboratories for novel physics in new parameter regimes, where quantum effects dominate thermal, and collisional relaxation effects are often small. Monte-Carlo methods provide an important tool for investigating the microscopic physics, but must be tied in with analytic phenomenology to yield any real understanding. Interfacial Helium provides an interesting two- dimensional thermodynamic system, and has remarkable and experimentally vital transport behavior that remains poorly understood.