In my talk I will discuss the non-equilibrium physics of the strongly correlated 
disordered one-dimensional electron system, described by the Luttinger liquid (LL) 
model. I will outline the kinetic approach to this model and present the kinetic 
equations for electron and plasmon distribution functions in the presence of 
impurities. It happens that at not too low temperature and bias voltage, the 
equilibration rate in this system is given by the elastic backscattering  rate, 
independent of the strength of electron-electron interaction, temperature, and bias.

In the second part of my talk I will discuss the tunneling into the non-equilibrium 
state of the LL, which is created as the result of electron backscattering leading 
to emission of non-equilibrium plasmons with typical frequency of the order of the 
bias voltage eU. The tunneling rates into/from such state are split into two edges: 
the edge exponent at the Fermi energy E_F is positive and is that of a bulk exponent 
in the equilibrium LL, while the edge exponent at E_F-eU turns out to be negative 
if Coulomb interaction is not too strong.

References:

[1] D. A. Bagrets, I. V. Gornyi, and D. G. Polyakov, Phys. Rev. B 80, 113403 (2009)
[2] S. Ngo Dinh, D.A. Bagrets, A.D. Mirlin, arXiv:0910.3917