A classical Luttinger liquid

Maura Sassetti

K.-V. Pham

The exact Green's functions of a Luttinger Liquid (LL) connected to impedances are computed at zero and finite temperature. It is also shown that if the resistances are equal to the characteristic impedance of the Luttinger liquid, then the finite Luttinger liquid connected to resistors is equivalent to an infinite Luttinger liquid. Impedance boundary conditions (IBC) include also as a special limit the case of open boundary conditions, which are explicitly recovered. Finally bosonization for a LL with IBC is proven to hold.

Michele Fabrizio

J. Silva-Valencia, E. Miranda, Raimundo R. dos Santos

We calculate the correlation functions and the dc conductivity of Luttinger liquid superlattices, modelled by a repeated pattern of interacting and free Luttinger liquids. In a specific realization, where the interacting subsystem is a Hubbard chain, the system exhibits a rich phase diagram with four different phases: two metals and two compressible insulators. In general, we find that the effective low-energy description amalgamates features of both types of liquids in proportion to their spatial extent, suggesting the interesting possibility of `engineered' Luttinger liquids. In recent years, new experimental techniques have made it possible to grow nanostructures which are topologically one-dimensional, such as quantum wires and Carbon nanotubes. However, care must be taken when invoking existing models to discuss their electronic properties, since inhomogeneities must be taken into account in a fundamental way. Consider, for instance, the Luttinger liquid (LL), which is the standard model for low-energy phenomena involving interacting electrons in one dimension [1]. The absence of conductance renormalization in long high-mobility GaAs wires [2] has been explained in terms of a usual LL (representing the wire) in contact with a non-interacting LL at each of its ends (representing the Fermi liquid leads); that is, overall, the system can be thought of as an inhomogeneous Luttinger Liquid (ILL). LLs with different inhomogeneity profiles have also been used in the context of the fractional quantum Hall effect (FQHE), to describe transitions between edge states at different fillings [3, 4], or between an edge state connected to a Fermi liquid [5]. A different class of inhomogeneous systems is represented by superlattices (SLs) and multilayers. By varying the relative th...

Luca D’Alessio, Armin Rahmani

We study the dynamics of a quantum-coherent thermally isolated Luttinger liquid with noisy Luttinger parameter. To characterize the fluctuations of the absorbed energy in generic noise-driven systems, we first identify two types of energy moments, which can help tease apart the effects of classical (sample-to-sample) and quantum sources of fluctuations. One type of moment captures the total fluctuations due to both sources, while the other one captures the effect of the classical source only. We then demonstrate that, in the Luttinger liquid case, the two types of moments agree in the thermodynamic limit, indicating that the classical source dominates. In contrast to equilibrium thermodynamics, in this driven system the relative fluctuations of energy do not decay with the system size. Additionally, we study the deviations of equal-time correlation functions from their ground-state value, and find a simple scaling behavior.