Momentum relaxation of strongly coupled impurities in quantum gases: A nonequilibrium Green's function approach

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 $\ensuremath{\tau}$ is governed entirely by the self-energy evaluated at zero momentum and zero frequency, $\mathrm{\ensuremath{\Sigma}}(\mathbf{p}=0;\ensuremath{\omega}=0)$. Furthermore, via virial expansion theory, $\ensuremath{\tau}$ admits a systematic expansion in powers of the fugacity $z\ensuremath{\equiv}{e}^{\ensuremath{\beta}\ensuremath{\mu}}$. The leading-order term precisely recovers the Boltzmann semiclassical result, while higher-order corrections capture quantum many-body effects beyond the semiclassical approximation.