Hierarchy, Dynamics and Memory Phenomena of Metastable States in Random Systems

在相互作用受挫的随机系统中，存在多个亚稳态，其自由能在一定相空间中具有复杂的多谷结构。在这个项目中，我们的目标是更深入地了解这些亚稳态的层次结构，以及与之相关的动力学和记忆现象。为此，我们详细地分析了几个自旋玻璃的平均场模型。准一维导体中的电荷密度波（CDW）系统表现出多种导电现象。我们也试图从CDW是一个具有自旋玻璃样随机性的非线性动力系统的观点来统一地理解它们。本文的分析基于Fukuyama-Lee-Rice （FLR）模型，该模型将CDW视为服从经典力学的连续体。本项目明确了以下几点：1。自旋玻璃的平均场模型：(1)SK模型的自由能结构是超尺度的，热激活过程对状态的弛豫遵循拉伸指数定律。(2)对sk模型进行适当的扩展，以提取每种材料中相互作用的特征特征，能够在一定程度上详细解释材料的自旋玻璃现象，如可重入跃迁。(3)在SK模型上得到的自旋玻璃图同样适用于“朴素”平均场模型，其中SK模型中的Onsager反应场被丢弃。CDW动力学：(1)FLR模型的非线性电导率对系统的维数表现出特征依赖性。其三维行为与实验结果相符。(2) CDW系统中的锁模现象可以解释为外部交流场诱导的协同锁模现象。(3)考虑热浴效应时，FLR模型中CDW电流的随机行为与最近观测到的窄带噪声峰宽度和1/f型宽带噪声的结果定性对应。这些现象被认为是由于系统在许多接近平稳结构的滑动构型之间的随机过渡引起的。少

In a random system with frustrations in its interactions there exist a number of metastable states, and its free energy seen in a certain phase space has complicated multi-valley structure. In this project we aimed to get deeper understandings on hierarchical structure of such metastable states, and on dynamics and memory phenomena associated with them. For this purpose we have analyzed in detail a few mean-field models for spin glasses. A charge-density-wave (CDW) system in quasi one-dimensional conductors exhibits a variety of electric conduction phenomena. We have also tried to understand them in a unified way from the view-point that the CDW is a nonlinear dynamical system with spin-glass-like randomness. The analyses here are based on the Fukuyama-Lee-Rice (FLR) model, in which the CDW is regarded as a continuum obeying classical mechanics. The following points are clarified in this project.1. Mean-Field Models of Spin Glasses:(1) The free energy structure of the SK model is in fa … More ct ultrametric, and the relaxation of a state by thermally activated processes obeys the stretched exponential law. (2) A proper extension of the sk model in such a way as to extract characteristic features of the interactions in each material is able to explain spin-glass phenomena, such as the re-entrant transition, of the material in certain detail. (3) The spin-glass picture derived on the SK model holds true also on the 'naive' mean-field model, in which Onsager's reaction field in the SK model is discarded.2. CDW Dynamics:(1) The nonlinear conductivity of the FLR model exhibits characteristic dependence on the dimensionality of the system. Its 3d behavior is compatible with experimental results. (2)Mode-locking phenomena in the CDW system can be interpreted as cooperative ones induced by the external ac field. (3) When the heat-bath effect is included, the stochastic behavior of the CDW current in the FLR model corresponds qualitatively to the recently observed results on the width of the narrow-band-noise peak and on the 1/f-type broad-band-noise. These phenomena are considered to originate from the stochastic transition of the system between many sliding configurations of the CDW which are close to a stationary one. Less