Transport thought a critical magnetic quantum dot away from equilibrium

LINK(+)

In this thesis, we investigate non-equilibrium phase transitions in a voltage-biased magnetic quantum dot, a minimal model relevant to spintronic devices near criticality. Using a Keldysh path-integral approach, we develop an effective theory for the dot's collective degrees of freedom under finite bias, $V$, connecting equilibrium and out-of-equilibrium regimes. We build a phase diagram for the system's steady-state magnetization, and find an open quantum critical point when , with fluctuations that diverge with in contrast with power-law scaling at finite and.

At weak drive, we extend the fluctuation–dissipation theorem to identify an effective temperature that governs the transition. At strong drive, this description breaks down: we uncover intrinsically non-equilibrium features, both away from criticality, such as oscillating power-law-correlated noise, and close to it, such as a crossover from first- to second-order transitions. Near criticality, we obtain a stochastic equation description for the order parameter dynamics, with a microscopically derived effective free energy that captures this crossover.

Our methods show that any finite bias permits a controlled semiclassical description, even beyond the effective-temperature regime. Using this framework, we show that fluctuations can stabilize metastable configurations in the strongly driven regime, revealing a subtle interplay between out-of-equilibrium noise and dissipation. Overall, our results help clarify how bias-induced driving and dissipation can shape classical and quantum criticality.