Dept. of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, United States.
Dept. of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, United States.
Adv Colloid Interface Sci. 2014 Jun;208:89-109. doi: 10.1016/j.cis.2014.02.017. Epub 2014 Feb 26.
Fluid lipid membranes can mediate forces between particles bound to them: A local deformation of the surface geometry created by some object spreads to distant regions, where other objects can respond to it. The physical characteristics of these geometric interactions, and how they are affected by thermal fluctuations, are well described by the simple continuum curvature-elastic Hamiltonian proposed 40 years ago by Wolfgang Helfrich. Unfortunately, while the underlying principles are conceptually straightforward, the corresponding calculations are not-largely because one must enforce boundary conditions for finite-sized objects. This challenge has inspired several heuristic approaches for expressing the problem in a point particle language. While streamlining the calculations of leading order results and enabling predictions for higher order corrections, the ad hoc nature of the reformulation leaves its domain of validity unclear. In contrast, the framework of Effective Field Theory (EFT) provides a systematic way to construct a completely equivalent point particle description. In this review we present a detailed account for how this is accomplished. In particular, we use a familiar example from electrostatics as an analogy to motivate the key steps needed to construct an EFT, most notably capturing finite size information in point-like "polarizabilities," and determining their value through a suitable "matching procedure." The interaction (free) energy then emerges as a systematic cumulant expansion, for which powerful diagrammatic techniques exist, which we also briefly revisit. We then apply this formalism to derive series expansions for interactions between flat and curved particle pairs, multibody interactions, as well as corrections to all these interactions due to thermal fluctuations.
由某个物体引起的表面几何形状的局部变形会扩散到遥远的区域，在那里其他物体可以对其做出响应。这些几何相互作用的物理特性，以及它们如何受到热涨落的影响，都可以通过 40 年前 Wolfgang Helfrich 提出的简单连续曲率弹性哈密顿量得到很好的描述。不幸的是，虽然基本原理在概念上是简单的，但相应的计算却很复杂——这主要是因为必须为有限大小的物体施加边界条件。这一挑战激发了几种启发式方法，以便用质点语言来表述这个问题。虽然简化了主导阶结果的计算，并能够对更高阶修正进行预测，但这种重构的任意性使其有效性域不明确。相比之下，有效场理论（EFT）框架为构建完全等效的质点描述提供了一种系统的方法。在这篇综述中，我们详细介绍了如何实现这一点。特别是，我们使用静电学中的一个熟悉例子作为类比，来激发构建 EFT 所需的关键步骤，特别是在点样“极化率”中捕捉有限大小的信息，并通过适当的“匹配程序”确定其值。然后，相互作用（自由）能作为一个系统的累积展开式出现，对于这个展开式，存在强大的图论技术，我们也将简要回顾这些技术。然后，我们将这一形式体系应用于推导平面和弯曲粒子对之间、多体相互作用以及所有这些相互作用由于热涨落而产生的修正的相互作用（自由）能的级数展开。
