Inelastic scattering effects on the inhomogeneous transverse conductivity of liquid metals and plasmas

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Abstract On the basis of the quantum Wigner density operator formalism for multicomponent charged particle systems, the wavenumber (k)- and frequency (ω)- dependent transverse conductivity σ^T (k,ω) of simple liquid metals is presented for homogeneous (k = 0) and inhomogeneous (k≠0) electric fields separately. The theory takes into account correlated density fluctuations of electrons and ions, with their mutual inelastic scattering being described by the ionic dynamic structure factors. Since homogeneous and inhomogeneous fields perturb the diagonal and off-diagonal elements of the density matrix, respectively, the corresponding transport equations exhibit a dissimilarity in their collision terms. In both cases, approximate solutions to the transport equations yield a conductivity of generalized Drude form characterized by the k- and ω-dependent complex relaxation time. It is shown that the k→0 limit of the inhomogeneous conductivity, σ^T (k→0,ω), coincides with the homogeneous one in classical ion regime such that βℏω_i≪1, where β is the inverse temperature and ω_i is a characteristic frequency of ionic density fluctuation; this condition may be satisfied for metals well above melting. At lower temperatures, it is suggested that the (homogeneous) DC conductivity σ(0) can exceed the (inhomogeneous) optical conductivity extrapolated to zero frequency, σ^T (k→0,0). This trend is qualitatively consistent with earlier observations for liquid polyvalent metals.