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

Abstract

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 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. Here, we study this violation and related out-of equilibrium phenomena in a single electron transistor with ferromagnetic leads, which can be tuned through a quantum phase transition. We review the breakdown of the fluctuation-dissipation theorem 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 fluctuation-dissipation theorem into the non-linear regime.