Hierarchy, Dynamics and Memory Phenomena of Metastable States in Random Systems
| Project/Area Number |
62540262
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物性一般（含極低温･固体物性に対する理論）
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| Research Institution | Kyoto University |
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Principal Investigator |
HAJIME TAKAYAMA Research Institute for Fundamental Physics, Kyoto University, 基礎物理学研究所, 教授 (40091475)
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| Project Period (FY) |
1987 – 1988
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| Project Status |
Completed (Fiscal Year 1988)
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| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 1988: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1987: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Mean-Field Theory of Spin Glasses / Ultrametricity of Metastable States / Re-entrant Transition / Naive Mean-Field Model / Nonlinear Dynamical System with Randomness / Mode-Locking Phenomena / Noises in CDW Current / CDW電流の確率的な振舞い / 自由エネルギーの多谷構造 / ナイーブ平均場模型 / 福山ーLeeーRice模型 / 準安定状態 / SK模型 / 超計量性 / 電荷密度波のダイナミックス / 福山-Lee-Rice模型 / モードロッキング / 狭帯域雑音 / 広帯域雑音 |
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| Research Abstract |
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
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Report
(3 results)
Research Products
(19 results)
