Abstract
The effect of dust size distribution in ultracold quantum dusty plasmas are investigated in this paper. How the dispersion relation and the propagation velocity for the quantum dusty plasma vary with the system parameters and the different dust distribution are studied. It is found that as the Fermi temperature of the dust grains increases the frequency of the wave increases for large wave number dust acoustic wave. The quantum parameter of Hd also increases the frequency of the large wave number dust acoustic wave. It is also found that the frequency ω0 and the propagation velocity ν0 of quantum dust acoustic waves all increase as the total number density increases. They are greater for unusual dusty plasmas than those of the usual dusty plasma.
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