基于晶格点缺陷的二维Frenkel-Kontorova模型耗散动力学研究

项目名称： 基于晶格点缺陷的二维Frenkel-Kontorova模型耗散动力学研究

项目编号： No.11304324

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 王苍龙

作者单位： 中国科学院近代物理研究所

项目金额： 25万元

中文摘要： 在相互作用多粒子体系的耗散动力学中，基于Frenkel-Kontorova模型开展共振现象和棘齿效应的研究有助于我们揭示许多物理和生物现象的本质规律。尤其当考虑晶格点缺陷时的研究在约瑟夫森结、电荷密度波、涡旋晶格和分子马达中具有广泛地应用。本研究拟针对含晶格点缺陷的二维Frenkel-Kontorova模型，借助分子动力学模拟技术，数值研究点缺陷在不同温度下的演化过程（如迁移、团簇和湮灭等）对Shapiro台阶和棘齿效应的影响。并获得Shapiro台阶和棘齿效应的内在联系，以及系统平均速度的解析表达形式。我们重点研究当系统外参数如系统温度、ac驱动力的振荡方式及其初相位、ac驱动力的振幅和频率等因素改变时，Shapiro台阶和棘齿效应的存在性和稳定性。作为技术方面的重要应用，我们的研究结果将在相互作用多粒子体系的实验和理论研究中具有现实指导意义和重要应用价值。

中文关键词： 共振现象；棘齿效应；点缺陷；Frenkel-Kontorova模型；

英文摘要： In the dissipative dynamics of the many-body systems with competing interactions, explorations of the resonant and ratchet effects of Frenkel Kontorova model may help us to understand the essence of many physical and biological phenomena. Particularly, in the presence of lattice point defects, the study could be important for the field of dissipative dynamics, such as Josephson junction, charge density waves, vortex lattice and biological motors. Based on molecular dynamical method, we will study the resonant and ratchet effect in the two dimensional Frenkel Kontorova model with the lattice point defects. We will study in detail the point defects dependence of the Shapiro steps and ratchet effects due to the migration, cluster and annihilation of the point defects in the enviroment of thermal noise. We will also analytically obtain the average velocity of the system when the resonant and ratchet effects occur. In the examination of the dissipative Frenkel Kontorova model, our interest is always focused on the existence and structural stability of the resonant and ratchet effects against the changing of the system parameters, such as the temperature, the oscillation mode and phase of the ac driven force and the frequency and amplitude of the ac driven. As the great significance of technical applications, the stud

英文关键词： resonant phenomena；ratchet effect；point defect；Frenkel-Konoraova model；