Capillary wave Hamiltonian

The fluctuations of the local interfacial position increase the effective area. This increase in area is associated with an increase of free energy Wwhich is proportional to the interfacial tension y. The free energy of a specific interface configuration u(r,) can be described by the capillary wave Hamiltonian ... 

A basic concept is then the interfacial stiffness and the description in terms of the capillary wave Hamiltonian (Privman, 1992). To introduce these terms, we consider the one-dimensional interface z = h(x) of a two-dimensional system for simplicity. Noting that in lattice systems the interfacial energy jnt will depend on the angle 9 between the tangent to the interface and the x-axis, we write 9 = arctanfdft/dx)]... 

The intrinsic structure of a liquid-vapor interface resembles the surface of a polymer liquid in contact with a nonattractive solid substrate at the pressure where the liquid coexists with its vapor. In the latter case, the system is in the vicinity of the drying transition and a layer of vapor intervenes between the substrate and the polymer liquid. There is, however, one important difference between the vapor-polymer interface and the behavior of a polymer at a solid substrate the local position of the interface can fluctuate. Let us first consider the case where the film is very thick and the solid substrate does not exert any influence on the free surface of the film in contact with its vapor. The fluctuations of the free surface are capillary waves. Neglecting bubbles or overhangs, one can use the position of the liquid-vapor interface, z = h x,y), as a function of the two lateral coordinates, x and y, parallel to the interface to describe the system configuration on a coarse scale. In this Monge representation, the free energy of the interface is given by the capillary-wave Hamiltonian " ... 

K. Rejmer and M. Napiorkowski, Curvature contributions to the capillary-wave Hamiltonian for a pinned Interface, Phys. Rev. E, 53, 881-895 (1996). 

The Hamiltonian which describes capillary waves as collective modes has the form ... 

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