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The effect of quantum recoil on the low-frequency electrostatic surface waves on a semi-bounded quantum turbulent plasma is investigated based on the kinetic dielectric permittivity of a plasma where the wave frequency is in the range of ion-acoustic wave. The dispersion relation and the damping rate of the surface wave are derived by employing the specular reflection boundary condition and the transverse truncation method. It is shown that the frequency of surface wave is enhanced by the quantum recoil for both non-degenerate and degenerate cases. The magnitude of damping rate is also increased by the quantum effect. The quantum recoil effect on the wave propagation is significantly reduced as the wave number becomes small. In the range of such small wave numbers, the diffusional dissipation becomes more important for the wave propagation.

Propagation of ion-acoustic surface waves in a turbulent quantum plasma with quantum recoil: transverse truncation method approach