Abstract:
We study the dynamics resulting out of an abrupt change of the two-particle interaction in two models of closed one-dimensional Fermi systems: (a) the field theoretical Tomonaga-Luttinger model and (b) a microscopic lattice model. Using a nonperturbative approach which is controlled for small two-particle interactions we are able to reach large times allowing us to access the properties of the steady state of the lattice model. Comparing those to the exact solution of the full dynamics in the Tomonaga-Luttinger model we provide evidence for universal Luttinger liquid behavior.

Abstract:
We study the energy transport between two interacting spin chains which are initially separated, held at different temperatures and subsequently put in contact. We consider the spin-1/2 XXZ model in the gapless regime and exploit its integrability properties to formulate an analytical Ansatz for the non-equilibrium steady state even at temperatures where the low-energy Luttinger liquid description is not accurate. We apply our method to compute the steady energy current and benchmark it both with the known low-energy limit and at higher temperatures with numerical simulations. We find an excellent agreement even at high temperatures, where the Luttinger liquid prediction is shown to fail.

Abstract:
We study the relaxation dynamics of the one-dimensional Tomonaga-Luttinger model after an interaction quench paying particular attention to the momentum dependence of the two-particle interaction. Several potentials of different analytical form are investigated all leading to universal Luttinger liquid physics in equilibrium. The steady-state fermionic momentum distribution shows universal behavior in the sense of the Luttinger liquid phenomenology. For generic regular potentials the large time decay of the momentum distribution function towards the steady-state value is characterized by a power law with a universal exponent which only depends on the potential at zero momentum transfer. A commonly employed ad hoc procedure fails to give this exponent. Besides quenches from zero to positive interactions we also consider abrupt changes of the interaction between two arbitrary values. Additionally, we discuss the appearance of a factor of two between the steady-state momentum distribution function and the one obtained in equilibrium at equal two-particle interaction.

Abstract:
We develop an operator-based approach to the problem of Luttinger liquid conductor in a non-equilibrium stationary state. We show that the coherent-state many-body fermionic density matrix as well as all fermionic correlation functions out of equilibrium are given by one-dimensional functional determinants of the Fredholm type. Thus, the model constitutes a remarkable example of a many-body problem where all the correlation functions can be evaluated exactly. On the basis of the general formalism we investigate four-point correlation functions of the fermions coming out of the Luttinger liquid wire. Obtained correlations in the fermionic distribution functions represent the combined effect of interaction and non-equilibrium conditions.

Abstract:
We study the relaxation dynamics of a nonequilibrium Luttinger liquid after a sudden interaction switch-on ("quench"), focussing on a double-step initial momentum distribution function. In the framework of the non-equilibrium bosonization, the results are obtained in terms of singular Fredholm determinants that are evaluated numerically and whose asymptotics are found analytically. While the quasi-particle weights decay exponentially with time after the quench, this is not a relaxation into a thermal state, in view of the integrability of the model. The steady-state distribution emerging at infinite times retains two edges which support Luttinger-liquid-like power-law singularities smeared by dephasing. The obtained critical exponents and the dephasing length are found to depend on the initial nonequilibrium state.

Abstract:
Photo-induced metallic states in a Mott insulator are studied for the half-filled, one-dimensional Hubbard model with the time-dependent density matrix renormalization group. An irradiation of strong AC field is found to create a linear dispersion in the optical spectrum (current-current correlation) in the nonequilibrium steady state reminiscent of the Tomonaga-Luttinger liquid for the doped Mott insulator in equilibrium. The spin spectrum in nonequilibrium retains the des Cloizeaux-Pearson mode with the spin velocity differing from the charge velocity. The mechanism of the photocarrier-doping, along with the renormalization in the charge velocity, is analyzed in terms of an effective Dirac model.

Abstract:
A point contact in a Luttinger liquid couples the left- and right-moving channels, producing shot noise. We calculate exactly the DC shot noise at zero temperature in the out-of-equilibrium steady state where current is flowing. Integrability of the interaction ensures the existence of a quasiparticle basis where quasiparticles scatter ``one by one'' off the point contact. This enables us to apply a direct generalization of the Landauer approach to shot noise to this interacting model. We find a simple relation of the noise to the current and the differential conductance. Our results should be experimentally-testable in a fractional quantum Hall effect device, providing a clear signal of the fractional charge of the Laughlin quasiparticles.

Abstract:
We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau's theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.

Abstract:
We develop a theory of tunneling spectroscopy of interacting electrons in a non-equilibrium quantum wire coupled to reservoirs. The problem is modelled as an out-of-equilibrium Luttinger liquid with spatially dependent interaction. The interaction leads to the renormalization of the tunneling density of states, as well as to the redistribution of electrons over energies. Energy relaxation is controlled by plasmon scattering at the boundaries between regions with different interaction strength, and affects the distribution function of electrons in the wire as well as that of electrons emitted from the interacting regions into non-interacting electrodes.

Abstract:
A one-dimensional system of interacting electrons out of equilibrium is studied in the framework of the Luttinger liquid model. We analyze several setups and develop a theory of tunneling into such systems. A remarkable property of the problem is the absence of relaxation in energy distribution functions of left- and right-movers, yet the presence of the finite dephasing rate due to electron-electron scattering, which smears zero-bias-anomaly singularities in the tunneling density of states.