Luttinger liquids have a power law dependence of resistance on temperature.

The theory of Luttinger liquids then predicts such behavior.

Among the hallmark features of a Luttinger liquid are the following:

Therefore, a 1-D conductor should behave as a Luttinger liquid instead.

Likewise, the tunneling rate into a Luttinger liquid is suppressed to zero at low voltages and temperatures, as a power law.

Even less familiar are Carbon nanotubes, the quantum wire and Luttinger liquid with their 1-dimensional topologies.

The simplest example of such a system is the system of interacting fermions in one-dimension, called Luttinger liquid.

Now, Luttinger liquids interest people working on superconductivity and on very small-scale semiconductors, where electrons' movements are indeed constrained.

A Luttinger liquid is a paramagnetic one-dimensional metal without Landau quasi-particle excitations.

Charge and spin waves are the elementary excitations of the Luttinger liquid, unlike the quasiparticles of the Fermi liquid (which carry both spin and charge).

Dr. Luttinger is best known for his work, begun in the 1960's, on what are called Luttinger liquids, theoretical models in which electrons are able to move in only one dimension instead of three.

A Tomonaga-Luttinger liquid, more often referred to as simply a Luttinger liquid, is a theoretical model describing interacting electrons (or other fermions) in a one-dimensional conductor (e.g. quantum wires such as carbon nanotubes).

Although Luttinger liquids are physically similar to Fermi liquids, the restriction to one dimension gives rise to several qualitative differences such as the absence of a quasiparticle peak in the momentum dependent spectral function and the presence of spin density waves.

He is known for a wide variety of fundamental contributions to condensed matter physics including the theory of Luttinger liquids, the theory of one dimensional Spin chains, the theory of Fractional Quantum Hall Effect, Exclusion Statistics, Entanglement Spectra and much more.