The quantum hydrodynamic model is used in this study to investigate electrostatic waves in a non-uniform, quantum magnetized dusty plasmas while accounting for dust gravitational effects. Quantum effects for dust grains are omitted, and ions and electrons are considered low-temperature Fermi gases. The generalized analytical dispersion relationship for the dust gravitation drift (DGD) wave is derived. The temperature dependence of the environment induces quantum effects which have been shown to have a significant impact on wave dispersion. In the absence of gravitational effects at high temperature, the fundamental dust drift mode has been reproduced. The criteria and the transitioning regimes are presented. Our findings apply to dense astrophysical objects such as the Enceladus encounter in the E ring of Saturn.
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