Transport in Luttinger Liquids

TL;DR

This paper reviews the theoretical understanding of electronic transport in Luttinger liquids, highlighting key phenomena like tunneling, persistent currents, and exact solvable models, emphasizing their relevance in quantum wire research.

Contribution

It introduces novel insights into transport in doubly-crossed Luttinger liquids and discusses an exactly solvable Luttinger-like model, advancing theoretical understanding.

Findings

Analysis of tunneling through barriers in quantum wires

Observation of persistent currents in mesoscopic rings

Development of an exactly solvable Luttinger-like model

Abstract

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 description of our own work on transport through doubly-crossed Luttinger liquids and transport in the Schulz-Shastry exactly solvable Luttinger-like model.