Structure of the effective Hamiltonian for liquid-vapor interfaces

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Abstract
Using the microscopic density-functional theory for inhomogeneous simple fluids, we derive a nonlocal and non-Gaussian expression for the effective Hamiltonian of a fluctuating liquid-vapor interface. If a gradient expansion is applied to this Hamiltonian, one obtains—after a partial resummation—as the leading term the standard effective interface Hamiltonian which is proportional to the increase of the area of the interface relative to that of the flat configuration. The next to leading terms are proportional to the Gaussian and to the mean curvature of the interface, respectively. Microscopic expressions for the coefficients in this expansion are derived. If the interparticle interactions in the fluid decay according to power laws, the gradient expansion breaks down. This is reflected in the nonanalytic behavior of the wave-vector-dependent surface tension which can be expressed in terms of the Fourier transform of the interaction potential between the fluid particles. Various approximations of the nonlocal Hamiltonian are compared quantitatively. The relevance of this Hamiltonian for interpreting scattering experiments is discussed.