Lifshitz theory of van der Waals pressure in dissipative media

We derive a first-principles method of determining the van der Waals or Casimir pressure in a dissipative and dispersive planar multilayered system by calculating the Maxwell stress tensor in a fictitious layer of vacuum, that is eventually made to vanish, introduced in the structure. This is illustrated by calculating the van der Waals pressure in a thin film with dissipative properties embedded between two semi-infinite media.

Figure 1

(a) A multilayer system with $N$ layers between two semi-infinite regions $L$ and $R$. (b) Method of splitting the $N$ layer multilayer system into components. The $z$ axis is perpendicular to the interfaces.

Figure 2

A four-layer system.