Nonequilibrium occupation number and charge susceptibility of a resonance level close to a dissipative quantum phase transition

Based on the recent paper (Phys. Rev. Lett. 102, 216803, (2009)), we study the nonequilibrium occupation number and charge susceptibility of a resonance level close to a dissipative quantum phase transition of the Kosterlitz-Thouless (KT) type between a de-localized phase for weak dissipation and a localized phase for strong dissipation. The resonance level is coupled to two spinless fermionic baths with a finite bias voltage and an Ohmic bosonic bath representing the dissipative environment. The system is equivalent to an effective anisotropic Kondo model out of equilibrium. Within the nonequilibrium Renormalization Group (RG) approach, we calculate nonequilibrium magnetization and spin susceptibility in the effective Kondo model, corresponding to occupation number and charge susceptibility of a resonance level, respectively. We demonstrate the smearing of the KT transition in the nonequilibrium magnetization as a function of the effective anisotropic Kondo couplings, in contrast to a perfect jump in magnetization at the transition in equilibrium. In the limit of large bias voltages, we find both quantities at the KT transition and in the localized phase show deviations from the equilibrium Curie-law behavior. As the system gets deeper in the localized phase, both quantities decrease more rapidly to zero with increasing bias voltages.