Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach

We derive formulas for the transverse electrical conductivity and the permittivity in a quantum collisional plasma using the kinetic equation for the density matrix in the relaxation approximation in the momentum space. We show that the derived formula becomes the classical formula when the Planck constant tends to zero and that when the electron collision rate tends to zero (i.e., the plasma becomes collisionless), the derived formulas become the previously obtained Lindhard formulas. We also show that when the wave number tends to zero, the quantum conductivity becomes classical. We compare the obtained conductivity with the conductivity obtained by Lindhard and with the classical conductivity.