  Equilibration to the steady state for a wide class of Luttinger liquid
ballistic weakly linked tunnel contacts is extensively studied. Quantum
fluctuations of tunnel current are considered in all orders in tunnel coupling
and out of the equilibrium in the time domain. Especially, two important
mathematical statements: Self-equilibration (SE-)theorem and Self-equilibration
(SE-)lemma on the exact re-exponentiation of thermal average from the
Keldysh-contour-ordered evolution operator for arbitrary weakly linked
Luttinger liquid tunnel contact are proven. Demonstrated proof of SE-theorem
and SE-lemma represents first evidence of a novel emergent phenomenon of
"self-equilibration" in the dynamics of quantum fluctuations of electron
transport through ballistic tunnel junctions. This phenomenon and all related
real-time full counting statistics are shown to be much more general as
compared to the usual Levitov-Lesovik scattering approach for the
non-interacting electrons, though SE-theorem also contains known results
obtained within the Levitov-Lesovik scattering approach as corresponding
limiting case for lowest order cumulants at $ g=1 $. As the result,
corresponding differential equation of "self-equilibration" for time-dependent
Keldysh partition function of tunnel contact is derived and explained. As the
consequence of obtained results, a universal character of self-equilibration of
tunnel current in one-dimensional weakly linked tunnel junctions is revealed
and studied on the level of non-equilibrium Fano factor. As well, a new measure
of disequilibrium in such systems - the "steady flow" rate - is also introduced
and discussed.
