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

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