  The charge transport and the noise of a quantum wire network, made of three
semi-infinite external leads attached to a ring crossed by a magnetic flux, are
investigated. The system is driven away from equilibrium by connecting the
external leads to heat reservoirs with different temperatures and/or chemical
potentials. The properties of the exact scattering matrix of this configuration
as a function of the momentum, the magnetic flux and the transmission along the
ring are explored. We derive the conductance and the noise, describing in
detail the role of the magnetic flux. In the case of weak coupling between the
ring and the reservoirs, a resonant tunneling effect is observed. We also
discover that a non-zero magnetic flux has a strong impact on the usual
Johnson-Nyquist law for the pure thermal noise at small temperatures.
