We develop and exploit an out-of-equilibrium theory, valid in arbitrary dimensions, which does not require initial thermalization. It is perturbative with respect to a weak time-dependent (TD) Hamiltonian term, but is nonperturbative with respect to strong coupling to an electromagnetic environment or to Coulomb or superconducting correlations. We derive unifying relations between the current generated by coherent radiation or statistical mixture of radiations, superimposed on a dc voltage
Vdc, and the out-of-equilibrium dc current which encodes the effects of interactions. We extend fully the lateral band-transmission picture, thus quantum superposition, to coherent many-body correlated states. This provides methods for a determination of the carrier's charge
q free from unknown parameters through the robustness of the Josephson-like frequency. We have derived similar relations for noise (I. Safi, arXiv:1401.5950) which have been exploited, recently, to determine the fractional charge in the fractional quantum Hall effect (FQHE) within the Jain series [M. Kapfer et al., Science (to be published)]. The present theory allows for breakdown of inversion symmetry and for asymmetric rates for emission and absorption of radiations. This generates rectification exploited here to propose methods to measure the charge
q, as well as spectroscopical analysis of the out-of-equilibrium dc current and the third cumulant of non-Gaussian source of noise. We also apply the theory to the Tomonaga-Luttinger liquid (TLL), showing a counterintuitive feature: A Lorentzian pulse superimposed on
Vdc can reduce the current compared to its dc value, at the same
Vdc, questioning the terminology ``photoassisted.'' Beyond a charge current, the theory applies to operators such as spin current in the spin Hall effect or voltage drop across a phase-slip Josephson junction.
We develop a general perturbative computation of finite-frequency quantum noise that applies, in particular, to both good or weakly transmitting strongly correlated conductors coupled to a generic environment. Under a minimal set of hypotheses, we show that the noise can be expressed through the nonequilibrium dc current only, generalizing a nonequilibrium fluctuation dissipation relation. We use this relation to derive explicit predictions for the nonequilibrium finite-frequency noise for a single channel conductor connected to an arbitrary Ohmic environment.
We derive fluctuation-dissipation relations for a tunnel junction driven through a resonator displaying strong quantum fluctuations. We find that the fluctuation-dissipation relations derived for classical external drives hold, provided the effect of the circuit's quantum fluctuations is incorporated into the modified nonlinear current voltage characteristics. We also demonstrate that all quantities measured under a time dependent bias can be reconstructed from their values measured under a dc bias using photoassisted tunneling relations. We confirm these predictions by implementing the circuit and measuring the dc current through the junction, its high frequency admittance, and its current noise at the frequency of the resonator.
We derive a novel fluctuation--dissipation theorem (FDT) valid for nonequilibrium initial states that imprint the braiding of anyons in the time domain. The derivation is carried out within the Unifying Nonequilibrium Perturbative Theory (UNEPT), which applies to both standard reservoir geometries and configurations with one or two quantum point contacts (QPCs) injecting dilute anyonic fluxes. Based on this FDT, we propose complementary methods to determine the time-domain braiding phase. The first method relates the DC backscattering noise to the integral of the current with respect to DC drives, while the second connects the AC current phase shift to the DC noise. The latter provides a particularly robust probe of the statistical angle
θ, offering an intrinsic calibration and cancelling certain nonuniversal renormalization effects. Specializing to a thermalized Tomonaga--Luttinger liquid (TLL), we further show that in the quantum regime the phase shift enables a direct determination of the scaling dimension
δ when
δ>1/2. These results define experimentally accessible schemes to extract either
θ or
δ in minimal single-QPC setups, without relying on interferometry or cross-correlation measurements.
We analyse the noise of the edge current of a generic fractional quantum Hall state in a tunnelling point contact system. We show that the non-symmetrized noise in the edge current for the system out-of-equilibrium is completely determined by the noise in the tunnelling current and the Nyquist-Johnson (equilibrium) noise of the edge current. Simply put, the noise in the tunnelling current does not simply add up the equilibrium noise of the edge current. A correction term arises associated with the correlation between the tunnelling current and the edge current. We show, using a non-equilibrium Ward identity, that this correction term is determined by the anti-symmetric part of the noise in the tunnelling current. This leads to a non-equilibrium fluctuation-dissipation theorem and related expressions for the excess and shot noise of the noise in the edge current. Our approach makes use of simple properties of the edge, such as charge conservation and chirality, and applies to generic constructions of the edge theory which includes edges of non-Abelian states and edges with multiple charged channels. Two important tools we make use of are the non-equilibrium Kubo formula and the non-equilibrium Ward identity. We discuss these identities in the appendix.
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,
Teff(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.