Yolcu Cem, Rothstein Ira Z, Deserno Markus
Department of Physics, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, Pennsylvania 15213, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011140. doi: 10.1103/PhysRevE.85.011140. Epub 2012 Jan 24.
We discuss an effective field theory (EFT) approach to the computation of fluctuation-induced interactions between particles bound to a thermally fluctuating fluid surface controlled by surface tension. By describing particles as points, EFT avoids computing functional integrals subject to difficult constraints. Still, all information pertaining to particle size and shape is systematically restored by amending the surface Hamiltonian with a derivative expansion. The free energy is obtained as a cumulant expansion, for which straightforward techniques exist. We derive a completedescription for rigid axisymmetric objects, which allows us to develop a full asymptotic expansion-in powers of the inverse distance-for the pair interaction. We also demonstrate by a few examples the efficiency with which multibody interactions can be computed. Moreover, although the main advantage of the EFT approach lies in explicit computation, we discuss how one can infer certain features of cases involving flexible or anisotropic objects. The EFT description also permits a systematic computation of ground-state surface-mediated interactions, which we illustrate with a few examples.
我们讨论一种有效场论（EFT）方法，用于计算受表面张力控制的、与热涨落流体表面结合的粒子之间的涨落诱导相互作用。通过将粒子描述为点，EFT避免了计算受困难约束的泛函积分。尽管如此，通过用导数展开修正表面哈密顿量，与粒子大小和形状相关的所有信息都能被系统地恢复。自由能通过累积量展开获得，对此存在直接的技术。我们推导出了刚性轴对称物体的完整描述，这使我们能够针对对相互作用，以距离倒数的幂次展开，得到完整的渐近展开。我们还通过几个例子展示了计算多体相互作用的效率。此外，尽管EFT方法的主要优势在于显式计算，但我们讨论了如何推断涉及柔性或各向异性物体的某些情况的特征。EFT描述还允许对基态表面介导的相互作用进行系统计算，我们用几个例子对此进行了说明。
