Bias driven non-equilibrium phase transitions

In this thesis, we investigated bias-driven non-equilibrium quantum phase transitions in a paradigmatic transport setup consisting of a quantum dot, with an interacting charging energy, connected to non-interacting leads. We mapped out the non-equilibrium zero-temperature phase diagram as a function of interaction strength and bias voltage across the dot.

Our central results are the behavior of charge susceptibility and current noise near the phase transition. Specifically, we show that zero-frequency current fluctuations become critical and diverge as near the non-equilibrium critical points. The charge susceptibility also diverges at the transition.

These results are achieved using a Random Phase Approximation (RPA). Additionally, we employ an Effective Stochastic Equation, developed by expanding the action to quadratic order in the fluctuations, which yields consistent results while offering a different physical interpretation.

We validated our findings in the high voltage limit, where the system-leads interaction becomes Markovian, using the Lindblad master equation. At this limit, both the average current and current noise coincide with those of a non-interacting system, consistent with the RPA effective field theory.

We used the Non-Crossing Approximation (NCA) to analyze the fermionic energy distribution beyond RPA despite its limitations in modeling the high-voltage regime. NCA predicts qualitative changes in the electronic distribution near the critical point, deviating substantially from Mean-Field predictions.

Our research demonstrates that current noise is a valuable tool for detecting and probing critical fluctuations at quantum critical points. It also opens new pathways for studying other types of non-equilibrium voltage-driven transitions.