Local conservation laws in ultracold Fermi systems with time-dependent interaction potential

In the context of an ultracold Fermi gas, we derive conservation laws for mass, energy and momentum based on a generalized nonlocal Boltzmann equation with gradient corrections in the collision integral. The corrections are expressed in terms of effective collision duration, particle displacement and changes of total momentum and energy. Their origin is in the in-medium T matrix. Using variations of the optical theorem, we show that in the collision integral the particle-hole symmetry can be recast into a form of collision symmetry amenable to semiclassical simulation. Pauli-blocked collisions are distinguished from Bose-stimulated nondissipative ones; the latter are not present in the absence of gradient corrections. Consolidating with the microscopic theory, we extract local conservation laws for a general time-dependent interaction potential, and demonstrate how both types of collisions affect densities and flows of conserving quantities. Comparison is made with the approach of Nozières and Schmitt-Rink in the limit of thermal equilibrium. Under approximations used for normal-state ultracold Fermi gases interacting via Feshbach resonances we demonstrate the effect of the collision delay on the shear viscosity.