LONG TIME CORRELATIONS OF NONLINEAR LUTTINGER LIQUIDS

Universal theory of nonlinear Luttinger liquids.

One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a linear one, which leads to a linear hydrodynamic theory. We show that to describe the measurable dynamic response functions one needs to take into account the no...

Fermi Liquids and Luttinger Liquids

Fractons and Luttinger liquids

We consider the concept of fractons as particles or quasiparticles which obey a specific fractal statistics in connection with a one-dimensional Luttinger liquid theory. We obtain a dual statistics parameter ν̃ = ν+1 which is identified with the controlling parameter e−2φ of the Luttinger model. In this way, a bosonic system characterized by a fractal index if [h] = if [2] = 1 is considered as a...

Ferromagnetic Luttinger liquids

We study weak itinerant ferromagnetism in one-dimensional Fermi systems using perturbation theory and bosonization. We find that longitudinal spin fluctuations propagate ballistically with velocity vm!vF , where vF is the Fermi velocity. This leads to a large anomalous dimension in the spin channel and strong algebraic singularities in the single-particle spectral function and in the transverse...

Transport in Luttinger Liquids

We give a brief introduction to Luttinger liquids and to the phenomena of electronic transport or conductance in quantum wires. We explain why the subject of transport in Luttinger liquids is relevant and fascinating and review some important results on tunneling through barriers in a one-dimensional quantum wire and the phenomena of persistent currents in mesoscopic rings. We give a brief desc...