Dynamics Associated with Metastable States in Random Systems

与随机系统中亚稳态相关的动力学

• 批准号: 60540227
• 负责人: TAKAYAMA Hajime
• 金额: $ 1.22万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60540227/
• 关键词: Metastable states; TAP theory; Parisi's theory; Dynamical mean field theory of spin glasses; Gabay-Toulouse transition; Dynamics of CDW; Hysteretic phenomena

1. Pure States and Parisi's Theory of the SK Spin Glass (SG) Model: A numerical method is established to find pure states, i.e., solutions for the TAP equations, of the SK model of a finite size. By the method the SG properties in the real spin space are examined in detail. On the other hand, a set of equations in Parisi's theory formulated in the replica spin space are also solved explicitly. Comparing both results obtained, we confirm quantitatively the basic relationships between the TAP theory and Parisi's one, and so make clear the unified picture of the SG transition within its mean field theory.2. Magnetic Field Effects on the SG Transition: (1) At the Gabay-Toulouse transition of the m-vector SK model under static field h, the transverse nonlinear susceptibility is shown not to diverge so long as h=0. (2) By means of the dynamical mean field theory it is shown that the SG phase does exist in an ac external field, though the transition temperature is lowered by the field.3. Dynamics of Charge-Density-Wave (CDW): Peculiar transport phenomena, observed in quasi 1D conductors and attributed to sliding motion of the CDW, are studied based on the Fukuyama-Lee-Rice (FLR) model, in which the CDW is regarded as classical deformable medium. (1) The results obtained by the perturbational expansion with respect to the pinning potential in the model are shown to agree with experimental results observed under large electric fields. (2) Extensive numerical simulations on 1, 2, and 3D FLR models are performed. They reproduce most of peculiar phenomena; dc nonlinear conduction, nonlinear dynamical phenomena such as the mode-locking, hysteretic phenomena revealing the existence of many metastable pinned states, and so on. The results confirm that these phenomena are characteristics of the FLR model, i.e., a nonlinear dynamical system with randomness.

1. SK自旋玻璃（SG）模型的纯态和Parisi理论：建立了一种寻找纯态的数值方法，有限尺寸SK模型的TAP方程的解。用这种方法详细地研究了真实的自旋空间中的SG性质。另一方面，Parisi理论中的一组方程在副本自旋空间中也得到了显式求解。通过对两种结果的比较，定量地证实了TAP理论与Parisi理论之间的基本关系，从而明确了SG跃迁在其平均场理论中的统一图景.磁场对SG跃迁的影响：（1）在静磁场h作用下，m矢量SK模型的Gabay-Toulouse跃迁，只要h=0，横向非线性极化率不发散。(2)利用动力学平均场理论，证明了在交流外场中存在SG相，但外场降低了相变温度.电荷密度波（CDW）动力学：基于Fukuyama-Lee-Rice（FLR）模型，将CDW视为经典的可变形介质，研究了准一维导体中由于CDW的滑动运动而产生的特殊输运现象。(1)通过微扰展开得到的钉扎势的模型中所得到的结果与大电场下观察到的实验结果一致。(2)对1、2和3D FLR模型进行了广泛的数值模拟。它们再现了FLR模型中的大部分奇特现象：直流非线性导电、锁模等非线性动力学现象、反映亚稳钉扎态存在的滞后现象等，证实了这些现象是FLR模型的特征，即：具有随机性的非线性动力系统。

项目成果

Hiroshi MATSUKAWA: "Numerical Study of Statics and Dynamics of Charge-Density-Waves Based on Fukuyama-Lee-Rice Model" Physica. 143B. 80-84 (1986)

Hiroshi MATSUKAWA：“基于 Fukuyama-Lee-Rice 模型的电荷密度波静力学和动力学的数值研究”物理学。

Hajime TAKAYAMA: "Dynamical Mean Field Theory of Spin Glasses and Their Phase Transitions in ac External Fields" Prog. Theor. Phys.Suppl. 87. 191-213 (1986)

Hajime TAKAYAMA：“自旋玻璃的动态平均场理论及其在交流外场中的相变”Prog。

Koji NEMOTO: J.Magn.Magn.Mater.54-57. 135-6 (1986)

Koji Nemoto：J.Magn.Magn.Mater.54-57。

Hiroshi MATSUKAWA: "Static and Dynamic Properties of Charge-Density-Waves Described by the Fukuyama-Lee-Rice Model. <I> . Perturbational Analysis and dc Nonlinear Properties" J. Phys. Soc. Japan. (1987)

Hiroshi MATSUKAWA：“Fukuyama-Lee-Rice 模型描述的电荷密度波的静态和动态特性。<I>。微扰分析和直流非线性特性”J. Phys。

Koji NEMOTO: J.Phys.C:Solid State Phys.18. L529-35 (1985)

Koji NEMOTO：J.Phys.C：固态物理学.18。