Abstract
The power spectrum of fluctuations thermally excited on the free surface of a simple liquid is calculated by looking for a solution of the linearized hydrodynamic equations which satisfy given initial conditions, specified by considerations of equilibrium statistical mechanics. To obtain the exact solution it is necessary to consider the equilibrium properties, not only of the liquid surface,but also of the fluid underneath. Furthermore we compute the response function of the surface to the action of an external sinusoidal pressure and verify the fluctuation-dissipation theorem. In certain damping conditions (near the critical damping), the power spectrum exhibits non-negligible deviations from the power spectrum of the displacement, for a thermally excited harmonic system. These differences are connected with the time delay with which a motion at the surface is felt underneath, and with the corresponding dissipation process. We show an experimental spectrum which is in good agreement with the predicted line shape.

第5、6篇貌似下不了

Etude expérimentale des ondes de capillarité excitées thermiquement a la surface d'un liquide pur pour des régimes hydrodynamiques proches de ..................