Nonlinear Luttinger liquid theory
Evaluation of the dynamic structure factors of one-dimensional quantum fluids consisting of particles with real, non-linear dispersion relation is a quite well-known problem. Its existence was appreciated for quite a while, but little progress was made, as the standard approach based on Tomonaga-Luttinger model proved to be frustratingly ineffective. We managed to solve the problem by establishing its relation to the physics of Fermi edge singularity. This relation especially transparent for weakly-interacting fermions, http://arxiv.org/abs/cond-mat/0603458, but may be extended to bosons in one dimension, arxiv.org/abs/0705.2015, http://arxiv.org/abs/0711.2697. Furthermore, the link to the Fermi edge singularity led to the construction of a universal phenomenological theory of nonlinear Luttinger liquid, http://arxiv.org/abs/0806.4779, http://arxiv.org/abs/0812.1046; it contains the conventional “linear” theory as a limit. The nonlinear Luttinger liquid theory is reviewed in a comprehensive Rev. Mod. Phys. review article, http://arxiv.org/abs/1110.1374.