Critical Charge and Current Fluctuations across a Voltage-Driven Phase Transition

Abstract

We investigate bias-driven non-equilibrium quantum phase transitions in a paradigmatic quantum-transport setup: an interacting quantum dot coupled to non-interacting metallic leads. Using the Random Phase Approximation, which is exact in the limit of a large number of dot levels, we map out the zero-temperature non-equilibrium phase diagram as a function of interaction strength and applied bias. We focus our analysis on the behavior of the charge susceptibility and the current noise in the vicinity of the transition. Remarkably, despite the intrinsically non-equilibrium nature of the steady state, critical charge fluctuations admit an effective-temperature description, $T_{\text{eff}}(T,V)$, that collapses the steady-state behavior onto its equilibrium form. In sharp contrast, current fluctuations exhibit genuinely non-equilibrium features: the fluctuation-dissipation ratio becomes negative in the ordered phase, corresponding to a negative effective temperature for the current degrees of freedom. These results establish current noise as a sensitive probe of critical fluctuations at non-equilibrium quantum phase transitions and open new directions for exploring voltage-driven critical phenomena in quantum transport systems.