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.