Inclusions in Fluctuating Membranes: Exact Results
Inclusions in Fluctuating Membranes: Exact Results
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波动膜中的夹杂物：精确结果
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发表时间：
1997
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通讯作者：
R. Netz
中科院分区：
文献类型：
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作者：
R. Netz
流体中的点状夹杂物，波动膜被认为是。在这里，术语“内含物”是在一般意义上使用的，描述了许多看似不同的情况：膜中的颗粒或其他外部和局部力（如激光镊子），这些力i）使膜局部更硬，ii）诱导局部自发弯曲，iii）改变局部膜厚度，或iv）相邻膜之间的局部分离。所有这些情况都可以用线性或二次局部扰动来描述，其中的配分函数是使用高斯膜模型精确计算的。因此，在没有进一步近似的情况下，获得了响应于一个夹杂物的存在的膜的变形形状和夹杂物之间的膜介导的相互作用。由线性扰动描述的两个夹杂物之间的相互作用与温度无关，因此不受膜波动的影响。两个夹杂物之间的相互作用所描述的二次扰动是完全由于膜形状的波动和消失在零温度下，在强耦合的限制，它显示了一个普遍的对数发散在短的长度尺度。公式的相互作用的n个夹杂物推导出，这表明非平凡的多体贡献的情况下，二次夹杂物。所有这些结果对所有温度和所有耦合强度都是有效的，因此桥接了先前在零温度（忽略膜形状波动）或使用微扰理论（对于夹杂物和膜之间的耦合强度小）获得的结果。这些精确结果是用一般的高斯哈密顿量得到的，因此适用于所有用高斯形式描述的系统。
Point-like inclusions in fluid, fluctuating membranes are considered. Here the term inclusion is used in a general sense and describes a number of seemingly disparate situations: particles in membranes or other external and localized forces (such as a laser tweezer) which i) make the membrane locally stiffer, ii) induce a local spontaneous curvature, iii) change the local membrane thickness, or iv) the local separation between neighboring membranes. All these situations can be described by linear or quadratic local perturbations, for which the partition function is calculated exactly using a Gaussian membrane model. The deformed shape of a membrane in response to the presence of one inclusion and the membrane-mediated interactions between inclusions are thus obtained without further approximations. The interaction between two inclusions described by linear perturbations is temperature independent and therefore not affected by membrane fluctuations. The interaction between two inclusions described by quadratic perturbations is solely due to membrane shape fluctuations and vanishes at zero temperatures; in the strong coupling limit it shows a universal logarithmic divergence at short length scales. Formulas for the interaction of n inclusions are derived, which show non-trivial multibody contributions for the case of quadratic inclusions. All these results are valid for all temperatures and for all coupling strengths and thus bridge previously obtained results obtained at zero temperatures (neglecting membrane shape fluctuations) or using perturbation theory (for small strengths of the coupling between the inclusions and the membrane). These exact results are obtained with general Gaussian Hamiltonians and are thus applicable to all systems described by Gaussians forms.