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，其自由能在一定的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种亚稳态的层次结构，以及与之相关的动力学和记忆现象。为此，我们详细分析了自旋玻璃的一些平均场模型。准一维导体中的电荷密度波（CDW）系统表现出多种导电现象。我们还尝试从 CDW 是一个具有类似自旋玻璃随机性的非线性动力系统的角度来统一理解它们。这里的分析基于 Fukuyama-Lee-Rice (FLR) 模型，其中 CDW 被视为遵守经典力学的连续体。本项目明确了以下几点： 1．自旋玻璃的平均场模型：(1) SK模型的自由能结构实际上是超度量的，并且热激活过程的状态弛豫遵循拉伸指数定律。 (2)对sk模型进行适当扩展，提取每种材料中相互作用的特征，能够在一定细节上解释材料的自旋玻璃现象，例如重入转变。 (3)基于SK模型导出的自旋玻璃图也适用于“朴素”平均场模型，其中SK模型中的Onsager反应场被丢弃。2． CDW动力学：(1)FLR模型的非线性电导率表现出对系统维数的特征依赖性。其 3d 行为与实验结果一致。 (2)CDW系统中的锁模现象可以解释为由外部交流场引起的协同现象。 (3) 当包括热浴效应时，FLR 模型中 CDW 电流的随机行为与最近观察到的窄带噪声峰宽度和 1/f 型宽带噪声结果定性对应。这些现象被认为源于系统在接近静止的 CDW 的许多滑动配置之间的随机转变。较少的

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