粗化过程中的有效迁移率和扩散率
Effective mobility and diffusivity in coarsening processes
摘要：
我们建议，粗化动力学可以描述在一个广义的随机游走，与漂移项，$μ(L)$，和扩散，${\cal D}(L)$控制的动态增长长度$L(t)$。我们将这种解释应用到一维伊辛模型的铁磁耦合常数按指数下降的规模$R$。在非守恒（Glauber）动力学的情况下，两项都存在，它们的平衡取决于$L(t)$和$R$之间的相互作用。在守恒（Kawasaki）动力学的情况下，漂移可以忽略不计，但${\cal D}(L)$强烈依赖于$L$。Glauber动力学的主要前渐近区表现为加速粗化，而Kawasaki动力学的主要前渐近区表现为减慢粗化。我们推断，在二维空间中也可以发现类似的行为。
英文摘要：
We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length $L(t)$ controlled by a drift term, $μ(L)$, and a diffusive one, ${\cal D}(L)$. We apply this interpretation to the one dimensional Ising model with a ferromagnetic coupling constant decreasing exponentially on the scale $R$. In the case of non conserved (Glauber) dynamics, both terms are present and their balance depend on the interplay between $L(t)$ and $R$. In the case of conserved (Kawasaki) dynamics, drift is negligible, but ${\cal D}(L)$ is strongly dependent on $L$. The main pre-asymptotic regime displays a speeding of coarsening for Glauber dynamics and a slowdown for Kawasaki dynamics. We reason that a similar behaviour can be found in two dimensions.
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