  In this work we discuss extensions of the pioneering analysis by
Dzyaloshinskii and Larkin of correlation functions for one-dimensional Fermi
systems, focusing on the effects of quasiparticle relaxation enabled by a
nonlinear dispersion. Throughout the work we employ both, the weakly
interacting Fermi gas picture and nonlinear Luttinger liquid theory to describe
attenuation of excitations and explore the fermion-boson duality between both
approaches. Special attention is devoted to the role of spin-exchange
processes, effects of interaction screening, and integrability. Thermalization
rates for electron- and hole-like quasiparticles, as well as the decay rate of
collective plasmon excitations and the momentum space mobility of spin
excitations are calculated for various temperature regimes. The phenomenon of
spin-charge drag is considered and the corresponding momentum transfer rate is
determined. We further discuss how momentum relaxation due to several competing
mechanisms, viz. triple electron collisions, electron-phonon scattering, and
long-range inhomogeneities affect transport properties, and highlight energy
transfer facilitated by plasmons from the perspective of the inhomogeneous
Luttinger liquid model. Finally, we derive the full matrix of thermoelectric
coefficients at the quantum critical point of the first conductance plateau
transition, and address magnetoconductance in ballistic semiconductor nanowires
with strong Rashba spin-orbit coupling.
