Model of resistances in systems of Tomonaga-Luttinger liquid wires

TL;DR

This paper extends a model for resistances in Tomonaga-Luttinger liquid wires, analyzing conductance in multi-wire systems with interactions, and reveals quantum effects that differ from classical resistance expectations.

Contribution

The paper introduces a comprehensive analysis of resistances and conductance in multi-wire Tomonaga-Luttinger systems, including spin interactions and complex junction configurations.

Findings

Total resistance differs from classical predictions in quantum wire systems.

Conductance depends on junction parameters and resistances, showing non-classical behavior.

Charge and spin conductances can be distinct in interacting electron systems.

Abstract

In a recent paper, we combined the technique of bosonization with the concept of a Rayleigh dissipation function to develop a model for resistances in one-dimensional systems of interacting spinless electrons [arXiv:1011.5058]. We also studied the conductance of a system of three wires by using a current splitting matrix M at the junction. In this paper we extend our earlier work in several ways. The power dissipated in a three-wire system is calculated as a function of M and the voltages applied in the leads. By combining two junctions of three wires, we examine a system consisting of two parallel resistances. We study the conductance of this system as a function of the M matrices and the two resistances; we find that the total resistance is generally quite different from what one expects for a classical system of parallel resistances. We will do a sum over paths to compute the conductance of this system when one of the two resistances is taken to be infinitely large. Finally we study the conductance of a three-wire system of interacting spin-1/2 electrons, and show that the charge and spin conductances can generally be different from each other.