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

这项研究的一部分是一个理论程序，用来研究非平衡系统在有限波数不稳定阈值附近的空间结构和复杂动力学。对静止不稳定性的研究已经取得了长足的进展，纯流体中的对流就是一个例子。二元流体混合物中的对流实验为动力学不稳定临界点附近的丰富行为的理论研究提供了动力。所使用的方法是微扰格式，导致“振幅”和“相”方程；全流体方程的数值解，以回答特定的问题；以及建立更简单的模型方程的数值模拟，以捕捉重要的物理不稳定性附近。虽然流体系统为理论和实验之间的仔细比较提供了便利的系统，但结果应该在不同的领域具有广泛的适用性。这项工作的另一部分将研究体氦和界面氦，这既是为了了解这些简单但具有挑战性的模型量子系统的微观行为，也是为了在新的参数区域将它们作为新物理的实验室进行研究，在新的参数区域，量子效应主导热学，而碰撞弛豫效应通常很小。蒙特卡罗方法为研究微观物理提供了一个重要的工具，但必须与分析现象学相结合才能产生真正的理解。界面氦提供了一个有趣的二维热力学系统，并具有显著的和实验上重要的输运行为，但仍然知之甚少。

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.