Junctions of three quantum wires and the dissipative Hofstadter model

TL;DR

This paper explores a quantum junction of three wires with magnetic flux, revealing complex conductance behaviors and connecting it to the dissipative Hofstadter model and string theory, highlighting novel fixed points and current flow asymmetries.

Contribution

It establishes a direct link between three-wire quantum junctions with flux and the dissipative Hofstadter problem, uncovering new fixed points and conductance properties.

Findings

Identification of non-trivial fixed points with chiral conductance

Discovery of asymmetric current flow at these fixed points

Connection to string theory in a background electromagnetic field

Abstract

We study a junction of three quantum wires enclosing a magnetic flux. This is the simplest problem of a quantum junction between Tomonaga-Luttinger liquids in which Fermi statistics enter in a non-trivial way. We present a direct connection between this problem and the dissipative Hofstadter problem, or quantum Brownian motion in two dimensions in a periodic potential and an external magnetic field, which in turn is connected to open string theory in a background electromagnetic field. We find non-trivial fixed points corresponding to a chiral conductance tensor leading to an asymmetric flow of the current.