重正化性化学机理的线索：噪声立方自催化模型的例子
Clues on chemical mechanisms from renormalizability: The example of a noisy cubic autocatalytic model
摘要：
研究了噪声对描述立方自催化化学反应的特定反应扩散系统方程组的重整化性的影响。我们使用的噪声是高斯的，在空间中具有幂律相关性，其特征在于幅度$A$和噪声指数$y$。我们表明，改变噪声指数是等效的替代$d_{s} \rightarrow d_{\rm eff} = d_{s} - y$，从而修改的发散结构的循环积分（$d_{s}$是空间的维数）。该模型对于$d_{\rm eff} < 6$在一个循环处可重正化，对于$d_{\rm eff} \geq 6$不可重正化。噪声产生的高阶相互作用的影响进行了讨论。特别是，我们展示了噪声如何诱导新的相互作用项，可以解释为一些（内部）“化学机制”的表现。我们还展示了如何思想的有效场论可以应用到构建一个更基本的化学模型，这个系统。
英文摘要：
We study the effect of noise on the renormalizability of a specific reaction-diffusion system of equations describing a cubic autocatalytic chemical reaction. The noise we are using is gaussian with power-law correlations in space, characterized by an amplitude $A$ and a noise exponent $y$. We show that changing the noise exponent is equivalent to the substitution $d_{s} \rightarrow d_{\rm eff} = d_{s} - y$ and thus modifies the divergence structure of loop integrals ($d_{s}$ is the dimension of space). The model is renormalizable at one-loop for $d_{\rm eff} < 6$ and nonrenormalizable for $d_{\rm eff} \geq 6$. The effects of noise-generated higher order interactions are discussed. In particular, we show how noise induces new interaction terms that can be interpreted as a manifestation of some (internal) "chemical mechanism". We also show how ideas of effective field theory can be applied to construct a more fundamental chemical model for this system.
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