non-equilibrium

phenomena in the condensed matter 

Study of many-body interacting systems out of equilibrium is both challenging and rewarding.  It deepens our  understanding  and  often  reveals  effects that are not present at equilibrium. A big progress  has been  made  after   the construction of the non-equilibrium bosonization  technique.
It  enabled us   to solve the tunneling spectroscopy problem for the non-equilibrium Luttinger liquid and to calculate  exactly  many-particle correlation functions of any order.  However there are important  questions in one dimensional physics that  lie  beyond Luttinger liquid paradigm  and require  new approaches.  The prototype problem of this kind is a quantum quench,  i.e. an evolution of a particles instantly released from the potential trap.   Even for the non interacting  electrons  the dynamics ( the movie shows the  density evolution – WP10k (1))   is surprisingly rich.

For the  interacting electrons this problem  can’t be described neither within the Fermi liquid nor within the Luttinger liquid paradigms.  We found,  that the  problem  exhibits  Fermi-Bose duality and can be mapped  into a weakly interacting  Fermi or Bose models by  non-linear unitary transformation.  In the movie  (Phase space of interacting fermions – population inversion ) one sees the formation of the  population inversion in the phase space of the “new  fermions”.  In terms of the original electrons the region of inverse populations  corresponds to an appearance of  “shock waves”,  solitons,  and the density ripples.

 

 

Dmitri Gutman