We consider a one-channel coherent conductor with a good transmission embedded into an ohmic environment whose impedance is equal to the quantum of resistance R_q=h/e^2 below the RC frequency. This choice is motivated by the mapping of this problem t
o a Tomonaga-Luttinger liquid with one impurity whose interaction parameter corresponds to the specific value K=1/2, allowing for a refermionization procedure. The new fermions have an energy-dependent transmission amplitude which incorporates the strong correlation effects and yields the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then we compute, for the first time, the finite-frequency differential conductance and the finite-frequency non-symmetrized noise. Contrary to intuitive expectation, both cannot be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission amplitude. Even more, the finite-frequency conductance obeys an exact relation in terms of the dc current which is similar to that derived perturbatively with respect to weak tunneling within the Tien-Gordon theory, and extended recently to arbitrary strongly interacting systems coupled eventually to an environment or/and with a fractional charge. We also show that the emission excess noise vanishes exactly above eV, even though the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages and frequencies below the RC frequency, and they allow to explore fully the quantum regime.
The dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect, is considered. Using perturbation theory, we first show that this rate has an anomalous dependence on the bias
voltage applied to the neighboring quantum point contact, because of the Luttinger liquid physics which describes the fractional Hall fluid. Next, we describe exactly the weak to strong backscattering crossover using the Bethe-Ansatz solution.
We consider the fluctuations of the electrical current (shot noise) in the presence of a voltage time-modulation. For a non-interacting metal, it is known that the derivative of the photo-assisted noise has a staircase behavior. In the presence of Co
ulomb interactions, we show that the photo-assisted noise presents a more complex profile, in particular for the two following systems: 1) a two-dimensional electron gas in the fractional quantum Hall regime for which we have obtained evenly spaced singularities in the noise derivative, with a spacing related to the filling factor and, 2) a carbon nanotube for which a smoothed staircase in the noise derivative is obtained.
