Bitbol Anne-Florence, Fournier Jean-Baptiste
Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, Paris 7 and UMR CNRS 7057, Paris, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061107. doi: 10.1103/PhysRevE.83.061107. Epub 2011 Jun 8.
We investigate the forces exerted on embedded inclusions by a fluid medium with long-range correlations, described by an effective scalar field theory. Such forces are the basis for the medium-mediated Casimir-like force. To study these forces beyond thermal average, it is necessary to define them in each microstate of the medium. Two different definitions of these forces are currently used in the literature. We study the assumptions underlying them. We show that only the definition that uses the stress tensor of the medium gives the sought-after force exerted by the medium on an embedded inclusion. If a second inclusion is embedded in the medium, the thermal average of this force gives the usual Casimir-like force between the two inclusions. The other definition can be used in the different physical case of an object that interacts with the medium without being embedded in it. We show in a simple example that the two definitions yield different results for the variance of the Casimir-like force.
我们研究了由有效标量场理论描述的具有长程关联的流体介质对嵌入其中的内含物施加的力。这类力是介质介导的类卡西米尔力的基础。为了研究这些超出热平均值的力，有必要在介质的每个微观状态中对其进行定义。目前文献中使用了两种不同的这些力的定义。我们研究了它们背后的假设。我们表明，只有使用介质应力张量的定义才能给出介质对嵌入内含物施加的所需力。如果第二个内含物嵌入介质中，该力的热平均值会给出两个内含物之间通常的类卡西米尔力。另一种定义可用于物体与介质相互作用但不嵌入其中的不同物理情形。我们在一个简单例子中表明，这两种定义对于类卡西米尔力的方差会产生不同结果。
