扩散限制侵蚀中的非局部亚共形不变性
Non-local meta-conformal invariance in diffusion-limited erosion
摘要：
通过精确求解扩散限制侵蚀过程（{ \sc dle}）的Langevin方程，研究了扩散限制侵蚀过程（{$d$ dle}）的非定常弛豫和物理老化。在$z=1$空间维中，亚共形李代数的一个新表示，同构于$a=b=d-1$，作为噪声平均{ \sc dle} Langevin方程的动力学对称.它的无穷小生成元在空间中是非局部的。从这个对称性的完整的时间-空间依赖的两个时间响应函数的{ \sc dle}的确切形式再现为$d=1$。讨论了与邻面阶跃扭折模型的关系。
英文摘要：
The non-stationary relaxation and physical ageing in the diffusion-limited erosion process ({\sc dle}) is studied through the exact solution of its Langevin equation, in $d$ spatial dimensions. The dynamical exponent $z=1$, the growth exponent $β=\max(0,(1-d)/2)$ and the ageing exponents $a=b=d-1$ and $λ_C=λ_R=d$ are found. In $d=1$ spatial dimension, a new representation of the meta-conformal Lie algebra, isomorphic to $\mathfrak{sl}(2,\mathbb{R})\oplus\mathfrak{sl}(2,\mathbb{R})$, acts as a dynamical symmetry of the noise-averaged {\sc dle} Langevin equation. Its infinitesimal generators are non-local in space. The exact form of the full time-space dependence of the two-time response function of {\sc dle} is reproduced for $d=1$ from this symmetry. The relationship to the terrace-step-kink model of vicinal surfaces is discussed.
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