INERTIAL AND DISSIPATIVE PROPERTIES OF SURFACE EXCITATIONS IN A FERMI-LIQUID

The kinetic properties of surface excitations in a Fermi liquid are considered, using the Vlasov equation for a Fermi system with a moving free surface. Expressions for the mass and friction coefficients for the collective variable describing the displacement of the surface of a semi-infinite system from the equilibrium position are obtained in the framework of a macroscopically self-consistent approach to the surface response function. The calculated kinetic coefficients agree with the results obtained in the classical limit from the quantum response function in the random-phase approximation. In the limit of an incompressible Fermi liquid the mass coefficient agrees (within a factor of order unity) with the expression for the mass coefficient in irrotational hydrodynamics. The velocity field corresponding to surface excitations of a Fermi liquid is rotational. The expression for the coefficient of friction agrees with the result obtained in Svyatetsky's phenomenological one-body dissipation theory. However, the coefficient of friction is calculated here with the same assumptions used in the treatment of collisionless Landau damping for zero sound in an infinite Fermi liquid.