Dynamics Associated with Metastable States in Random Systems

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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.