Abstract
We perform a time-dependent local spin density approximation (TDLSDA) study of one-dimensional Fermions with a contact interaction. We show that the simple TDLSDA approximation provides an exact description for density and spin density modes and conductance $G$ in one-dimensional quantum wires, by establishing a general equivalence between TDSLDA and Tomonaga-Luttinger model for the elementary excitation spectra in one-dimensional Fermi systems. The role of interaction effects is carefully analyzed especially in relation to the problem of the universality of the result $G=2{e}^{2}/h$ for the conductance of one-dimensional systems. Finally our results are in good agreement with the available experimental data on the one-dimensional plasmon dispersion, and conductance in GaAs quantum wires.
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