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，我们详细分析了几种自旋玻璃平均场模型。准一维导体中的电荷-密度-波(CDW)系统表现出各种导电现象。我们还试图从CDW是一个具有自旋玻璃随机性的非线性动力系统的观点出发，以统一的方式理解它们。这里的分析是基于福山-李-赖斯(FLR)模型，其中CDW被视为服从经典力学的连续体。在这个项目中澄清了以下几点。自旋玻璃平均场模型：(1)SK模型的自由能结构为FA…Ct越多，热激活过程对态的驰豫就越符合伸展指数定律。(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，能够较详细地解释材料的自旋玻璃现象，如再入相变。(3)在SK模型上得到的自旋玻璃图在“朴素”平均场模型上也是成立的，在该模型中丢弃了SK模型中的Onsager反作用力。CDW动力学：(1)FLR模型的非线性电导率表现出对系统维度的特征依赖关系。它的3D行为与实验结果相一致。(2)CDW系统中的锁模现象可以解释为外加交流电场引起的合作锁模现象。(3)当考虑热浴效应时，FLR模型中CDW电流的随机行为与最近关于窄带噪声峰宽度和1/f型宽带噪声的观测结果定性地一致。这些现象被认为源于系统在CDW的许多滑动构形之间的随机转变，这些滑动构形接近于静止的一个。较少

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