发表机构
Instituto de Física Fundamental, CSIC（西班牙科学理事会基础物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该论文推导了表面扩散中密度波衰减的精确记忆方程，建立了局部速率求和规则，并证明长波长下有效跳跃速率与热力学因子的乘积关系，为自旋回波实验提供了理论框架。
AI 中文摘要
相互作用吸附层中密度波的衰减遵循莫里形式的精确记忆方程。作为守恒密度的傅里叶分量，其相关函数是特征函数，而核由第二个特征函数（即单次跳跃的特征函数）构建。局部速率服从一个求和规则，其动量依赖性为1减去单次跳跃的特征函数，再除以静态结构因子。细致平衡使衰减成为非负权重弛豫模式的叠加，其矩为静态平衡平均值，因此相关连分数的截断构成收敛的封闭形式层级，每一项都是衰减本身的一个界限。研究表明，拟合返回的单一速率是瞬时速率在时间窗口内的平均值，因此绝不会超过局部速率。在长波长下，两者重合，弛豫谱在此分离，一个集体模式几乎占据密度波的全部权重，而通常拟合自旋回波数据的单指数即为衰减本身。实验在每个波矢处所达到的也是衰减下的面积，即相关时间。它与静态结构因子和单次跳跃几何一起，构成一个组合，理论将其识别为有效跳跃速率除以局部速率与相关时间的乘积。该乘积从不低于1，并且在长波长下趋于1，只要吸附粒子离开某位点的速率与其离开的目的地无关。在水动力极限下，求和规则变为达肯型关系，其中速率乘以热力学因子为有效跳跃速率，而非标记吸附粒子的迁移率。
英文摘要
The decay of a density wave in an interacting adlayer obeys an exact memory equation of Mori's form. Being a Fourier component of a conserved density, its correlation function is a characteristic function, and the kernel is built from a second one, that of a single jump. The local rate obeys a sum rule whose momentum dependence is one minus the characteristic function of a single jump, divided by the static structure factor. Detailed balance makes the decay a superposition of relaxation modes of non-negative weight whose moments are static equilibrium averages, so that the truncations of the associated continued fraction form a convergent hierarchy of closed forms, each of them a bound on the decay itself. The single rate a fit returns is shown to be the mean of the instantaneous rate over a time window, hence never above the local rate. At long wavelength, the two coincide, the relaxation spectrum separating there, one collective mode taking almost the whole weight of the density wave and the single exponential usually fitted to spin-echo data being the decay itself. What an experiment reaches at every wavevector is also the area under the decay, a correlation time. Together with the static structure factor and the single-jump geometry, it forms one combination which the theory identifies with the effective hop rate divided by the product of the local rate and the correlation time. That product never falls below unity and tends to unity at long wavelength whenever the rate at which an adparticle leaves a site is independent of the site it leaves for. In the hydrodynamic limit, the sum rule becomes a relation of Darken type in which the rate multiplied by the thermodynamic factor is the effective hop rate and not the mobility of a labelled adparticle.
Comments20 pages; 1 figure; 1 table
