  The nonequilibrium tunnelling center model of a localized electronic level
coupled to a fluctuating two-state system and to two electronic reservoirs, is
solved via an Anderson-Yuval-Hamann mapping onto a plasma of alternating
positive and negative charges time-ordered along the two "Keldysh" contours
needed to describe nonequilibrium physics. The interaction between charges
depends both on whether their time separation is small or large compared to a
dephasing scale defined in terms of the chemical potential difference between
the electronic reservoirs and on whether their time separation is larger or
smaller than a decoherence scale defined in terms of the current flowing from
one reservoir to another. A renormalization group transformation appropriate to
the nonequilibrium problem is defined. An important feature is the presence in
the model of a new coupling, essentially the decoherence rate, which acquires
an additive renormalization similar to that of the energy in equilibrium
problems. The method is used to study interplay between the dephasing-induced
formation of independent resonances tied to the two chemical potentials and the
decoherence which cuts off the scaling and leads to effectively classical
long-time behavior. We determine the effect of departures from equilibrium on
the localization-delocalization phase transition.

Mesoscale and Nanoscale Physics