On the solutions of Landau transport equations in one-dimension and their equivalence with the Tomonaga–Luttinger model predictions

By using linear response theory, we show that Landau transport equations in one-dimension (1D) and Tomonaga–Luttinger model provide exactly the same description for density and spin-density modes and conductance in 1D systems. Landau transport equations in 1D can be derived rigorously from the time-dependent Hartree and adiabatic time-dependent local spin density (TDLSDA) theories without making use of the concept of Landauʹs quasi-particles. In 1D, in the long wavelength limit, there is a perfect equivalence between Landau and the random-phase-approximation (RPA) and TDLSDA responses.