The low-energy properties of one-dimensional (1D) fermions in clean quantum wires are described by the canonical Tomonaga-Luttinger model. This model rests on the linearization of the fermion spectrum $E(k) = k2/2m –> E_F ± v_F (k -/+ k_F)$ close to the Fermi points $+/- k_F$ ($v_F$ is the Fermi velocity and $E_F$ is the Fermi energy). Such an approximation allows to map the system of interacting fermions on a system of free bosons offering an elegant non-perturbative technique (bosonization) to deal with problems of 1D interacting fermions. However, effects such as plasmon damping, Coulomb drag and fermion relaxation in clean quantum wires do not manifest in the linear approximation. Any quantitative analysis of these important physical phenomena requires taking into account the full non-linear fermion spectrum ($E(k) = k2/2m$). In order to quantitatively take into account of the curvature of the spectrum I will then proceed along two roads: 1) start from usual bosonization and add non-linear terms to emulate spectrum curvature (the bosons are then no more free hence the bosonization is termed non-linear) 2) start from the original fermions with curved spectrum and develop a diagrammatic approach to compute their properties. Model 1) has been used in the literature and I will focus on some of its limitations. Model 2) on the other hand is new; I will present its technical implementation to the computation of curvature corrections to the density-density correlation function and some of its applications with respect to plasmon damping and fermion relaxation in clean quantum wires.

ICTP Trieste)