Within the nonequilibrium Green's function framework, we systematically analyze the momentum relaxation dynamics of strongly coupled impurities in three-dimensional nondegenerate quantum gases. Using the Hartree-Fock approximation, we establish that the impurity velocity exhibits exponential decay asymptotically. When the impurity velocity is much lower than the thermal velocity of the gas atoms, the relaxation time $\tau$ is governed entirely by the self-energy evaluated at zero momentum and zero frequency, $\mathrm{\Sigma }(\mathbf{p}=0;\omega =0)$. Furthermore, via virial expansion theory, $\tau$ admits a systematic expansion in powers of the fugacity $z\equiv e^{\beta \mu }$. The leading-order term precisely recovers the Boltzmann semiclassical result, while higher-order corrections capture quantum many-body effects beyond the semiclassical approximation.

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• Nonequilibrium statistical mechanics
• Ultracold gases
• Cluster expansion
• Diagrammatic methods
• Nonequilibrium Green's function