On the concept of effective temperature in current carrying quantum critical states

Quantum criticality has attracted considerable attention both theoretically and experimentally as a way to describe part of the phase diagram of strongly correlated systems. A scale-invariant fluctuation spectrum at a quantum critical point (QCP) implies the absence of any intrinsic scale. Any experimental probe may therefore create an out-of-equilibrium setting; the system would be in a non-linear response regime, which violates the fluctuation-dissipation theorem (FDT). Here, we study this violation and related out-of equilibrium phenomena in a single electron transistor (SET) with ferromagnetic leads, which can be tuned through a quantum phase transition. We review the breakdown of the FDT and study the universal behavior of the fluctuation dissipation relation of various correlators in the quantum critical regime. In particular, we explore the concept of effective temperature as a means to extend the FDT into the non-linear regime.