Model of resistances in systems of Tomonaga-Luttinger liquid wires

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.

11 pages, 9 figures

References in corpus (14)

• Coulomb drag by small momentum transfer between quantum wires
• Junctions of anyonic Luttinger wires
• Junctions of three quantum wires for spin 1/2 electrons
• Y-junction of superconducting Josephson chains
• Enhancement of tunneling density of states at a junction of three Luttinger liquid wires
• Frustration of decoherence in $Y$-shaped superconducting Josephson networks
• Resistivity of inhomogeneous quantum wires
• Quantum Fields on Star Graphs with Bound States at the Vertex
• Line junction in a quantum Hall system with two filling fractions
• A minimal model of quantized conductance in interacting ballistic quantum wires
• Electronic transport in inhomogeneous quantum wires
• Conductance of Tomonaga-Luttinger liquid wires and junctions with resistances
• Power dissipation for systems with junctions of multiple quantum wires
• Off-critical Luttinger Junctions

Cited by in corpus (5)

• Enhancement of crossed Andreev reflection in a superconducting ladder connected to normal metal leads
• Enhancement of tunneling density of states at a Y junction of spin-1/2 Tomonaga Luttinger liquid wires
• Efficient Density Matrix Renormalization Group algorithm to study Y-Junctions with integer and half-integer spin
• Theory of the conductance of interacting quantum wires with good contacts and applications to carbon nanotubes
• Time resolved transport properties of a $Y$-junction of Tomonaga-Luttinger liquids