d+1维生长方程的奇异动力学标度性质研究

ANOMALOUS DYNAMIC SCALING OF THE (d+1)-DIMENSIONAL GROWTH EQUATIONS

将López基于Hentschel和Family的直接标度分析理论提出的判别连续性动力学生长方程标度奇异性的解析方法,本文推广应用到d+1维生长方程动力学标度奇异性质的研究中,分别判断出d+1维的Kardar-Parisi-Zhang(KPZ)、线性molecular-beam epitaxy(MBE)、Sun-Guo-Grant(SGG)以及Lai-Das Sarma-Villain(LDV)等生长方程在弱耦合和强耦合区域内的奇异标度性质.当生长方程出现奇异标度性质时,使用标度关系lαoc=α-zκ可以得到各方程的局域粗糙度指数,并与数值模拟的结果相吻合.

Based on the scaling analysis introduced by Hentschel and Family, Lopez proposed an analytical approach to determine anomalous dynamic scaling of the continuum growth equations. In this work, the approach is generalized to the （d＋ 1）-dimensional growth equations to determine their dynamic scaling. The growth equations studied here include （d＋ 1）-dimensional Kardar-Parisi-Zhang（KPZ）, linear molecular beam epitaxy （MBE）, Sun-Guo-Grant （SGG） and Lai-Das Sarma-Villain （LDV） equation. Their anomalous scaling properties are obtained in both the weak- and strong-coupling regions respectively. When these growth equations exhibit anomalous dynamic scaling, the local roughness exponents are obtained by using scaling relation αloc=α-zk, which are well consistent with the corresponding numerical results.