Fluctuations in the structure of interfaces

We study the stability matrix (the matrix of second derivatives of the free energy functional with respect to the density at each point in the system) for various phenomenological models of interfaces between coexisting phases. The eigenvectors and eigenvalues of that matrix are the eigenmodes, and their inverse susceptibilities, of fluctuations of the interface. We find that, due to the presence of the interface, several discrete eigenvalues typically appear in addition to the continuous bands of eigenvalues of the bulk phases. Some features appear to be generic, while others depend on the details of the model.