论文标题
几乎球形膜的热波动的统计力学：弯曲和拉伸弹性的影响
Statistical mechanics of thermal fluctuations of nearly spherical membranes: the influence of bending and stretching elasticities
论文作者
论文摘要
综述了对热激发系统的典型示例的几乎球形囊泡和微乳液液滴的理论研究。我们考虑受固定面积$ a $和固定体积$ v $约束的系统的形状波动，其几何形状是根据标量球形谐波呈现的。这些约束可以以不同的方式纳入理论中。在对这两种方法进行了介绍之后：由Delta功能膜区域$ a $ a $ [Seifert，Z。Phys。 B，97，299，（1995）]或通过Lagrange乘数$σ$近似为$ a $ a [Milner and Safran，Phys。 Rev. A，36，4371（1987）]，我们讨论了拉伸效应的确定作用，该作用已在包含拉伸能量术语的模型的框架中宣布，该模型通过膜囊泡张力表示[Bivas and Tonchev，phys.rev.e，100，022416（2019）]。由于已经开发了基于Bogoliubov的自由能的不平等现象的近似方法，因此二手汉密尔顿的波动频谱已经开发出来。最后一种方法中的区域约束似乎是膜张力的自洽方程。在一般情况下，该方程在分析上是棘手的。但是，可以对背后的物理学有很多深入的了解，要么对模型参数的值施加一些限制，要么研究限制案例，在该案例中，在其中解决了自洽方程。也讨论了对合奏对等效的含义。
Theoretical studies of nearly spherical vesicles and microemulsion droplets, that present typical examples for thermally-excited systems that are subject to constraints, are reviewed. We consider the shape fluctuations of such systems constrained by fixed area $A$ and fixed volume $V$, whose geometry is presented in terms of scalar spherical harmonics. These constraints can be incorporated in the theory in different ways. After an introductory review of the two approaches: with an exactly fixed by delta-function membrane area $A$ [Seifert, Z. Phys. B, 97, 299, (1995)] or approximatively by means of a Lagrange multiplier $σ$ conjugated to $A$ [Milner and Safran, Phys. Rev. A, 36, 4371 (1987)], we discuss the determined role of the stretching effects, that has been announced in the framework of a model containing stretching energy term, expressed via the membrane vesicle tension [Bivas and Tonchev, Phys.Rev.E, 100, 022416 (2019)]. Since the fluctuation spectrum for the used Hamiltonian is not exactly solvable an approximating method based on the Bogoliubov inequalities for the free energy has been developed. The area constraint in the last approach appears as a self-consistent equation for the membrane tension. In the general case this equation is intractable analytically. However, much insight into the physics behind can be obtained either imposing some restrictions on the values of the model parameters, or studying limiting cases, in which the self-consistent equation is solved. Implications for the equivalence of ensembles have been discussed as well.
