Longitudinal electric conductivity in a quantum plasma with a variable collision frequency in the framework of the Mermin approach

In the framework of the Mermin approach, we obtain formulas for the longitudinal electric conductivity in a quantum collisional plasma with a collision frequency depending on the momentum. We use a kinetic equation in the momentum space in the relaxation approximation. We show that as the Planck constant tends to zero, the derived formula transforms into the corresponding formula for a classical plasma. We also show that as the frequency of collisions between plasma particles tends to zero (the plasma transforms into a collisionless plasma), the derived formula transforms into the well-known Klimontovich–Silin formula for the collisionless plasma. We show that if the collision frequency is constant, then the derived formula for the permittivity transforms into the well-known Mermin formula.