Electronic viscosity in a quantum well: A test for the local-density approximation

In the local-density approximation (LDA) for electronic time-dependent current-density-functional theory, many-body effects are described in terms of the viscoelastic constants of the homogeneous three-dimensional electron gas. In this paper, we critically examine the applicability of the three-dimensional LDA to the calculation of the viscous damping of one-dimensional collective oscillations of angular frequency ω in a quasi-two-dimensional quantum well. We calculate the effective viscosity ζ(ω) from perturbation theory in the screened Coulomb interaction and compare it with the commonly used three-dimensional LDA viscosity Y(ω). Significant differences are found. At low frequency, Y(ω) is dominated by a shear term, which is absent in ζ(ω). At high frequency, ζ(ω) and Y(ω) exhibit different power-law behaviors (ω⁻³ and ω^−5∕2, respectively), reflecting different spectral densities of electron-hole excitations in two and three dimensions. These findings demonstrate the need for better approximations for the exchange-correlation stress tensor in specific systems where the use of the three-dimensional functionals may lead to unphysical results.