论文标题
动力学化学:反应流体的非平衡有效作用
Dynamical chemistry: non-equilibrium effective actions for reactive fluids
论文作者
论文摘要
我们提供了两种描述在流体相中发生的化学反应的方法。第一种方法反映了通过保守的---或为了说明化学反应(未经保存的 - - 电流与局部平衡参数)的通常推导运动运动方程。第二种方法涉及一种更高的方法,我们从非平衡有效场理论(EFT)的角度攻击了相同的问题。使用Schwinger-keldysh轮廓上的内形式主义定义了非平衡有效作用,因此能够描述热波动和耗散以及量子效应。非平衡EFT方法特别有力,因为该动作中的所有术语均由系统的对称性完全指定。特别是,热力学的第二定律不需要手工包含,而是从动作本身中得出的。我们发现两种方法产生的运动方程都一致,但是EFT方法产生了某些优势。为了证明其中一些优势,我们构建了一种二次作用,该作用对非常小的距离尺度有效 - - 比普通流体动力学分解的量表小得多。这样的动作捕获了反应的全部热力学和量子行为,并以二次顺序扩散。最后,采用低频和低波动限度的限制,我们将众所周知的反应扩散方程的线性化版本作为最终相干检查。
We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved---or to account for chemical reactions, non-conserved---currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in-in formalism on the Schwinger-Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales---much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction-diffusion equations as a final coherence check.