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Pairing Fluctuation Corrections to the Kinetic Theory of Liquid $^3\mathrm{He}$

Liquid $^3\mathrm{He}$ is a Fermi liquid that undergoes a BCS-type phase transition to a spin-triplet superfluid, making it valuable for understanding interacting fermions. When the temperature approaches the transition temperature $T_{\mathrm{c}}$ from above, physical properties can be modified by Cooper pair fluctuations, leading to deviations from the predictions of Fermi liquid theory. We use nonequilibrium Green's function theory to study the role of pair fluctuations on quasiparticle transport. The Boltzmann-Landau kinetic equation, which describes the transport properties of Fermi liquids, acquires corrections from the interaction of quasiparticles with pair fluctuations. As an application, we study the effects of pair fluctuations on the propagation of zero sound in liquid $^3\mathrm{He}$. We calculate the temperature-dependent correction to the zero sound velocity due to pair fluctuations, and compare the result with existing experimental data.