  We study a junction of three quantum wires enclosing a magnetic flux. The
wires are modeled as single-channel spinless Tomonaga-Luttinger liquids. This
is the simplest problem of a quantum junction between Tomonaga-Luttinger
liquids in which Fermi statistics enter in a non-trivial way. We study the
problem using a mapping onto the dissipative Hofstadter model, describing a
single particle moving on a plane in a magnetic field and a periodic potential
coupled to a harmonic oscillator bath. Alternatively we study the problem by
identifying boundary conditions corresponding to the low energy fixed points.
We obtain a rich phase diagram including a chiral fixed point in which the
asymmetric current flow is highly sensitive to the sign of the flux and a phase
in which electron pair tunneling dominates. We also study the effects on the
conductance tensor of the junction of contacting the three quantum wires to
Fermi liquid reservoirs.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;High Energy Physics - Theory