Transport through a one-dimensional wire of interacting electrons connected to semi-infinite leads is investigated using a bosonization approach. An incident electron is transmitted as a sequence of partial charges. The dc conductance is found to be entirely determined by the properties of the leads. The dynamic nonlocal conductivity is rigorously expressed in terms of the transmission. For abrupt variations of the interaction parameters at the junctions the central wire acts as a Fabry-Perot resonator. When one of the connected wires has a tendency towards superconducting order, partial Andreev reflection of an incident electron occurs. 73.40.Jn, 74.80.Fp Typeset using REVT E X 1
It is shown that a one-channel coherent conductor in an ohmic environment can be mapped to the problem of a backscattering impurity in a Tomonaga-Luttinger liquid (TLL). This allows to determine non perturbatively the effect of the environment on I − V curves, and to find an exact relationship between dynamic Coulomb blockade and shot noise. We investigate critically how this relationship compares to recent proposals in the literature. The full counting statistics is determined at zero temperature.PACS numbers: 73.23.Hk,73.63.Rt,72.70.+m, A mesoscopic conductor embedded in an electrical circuit forms a quantum system violating Ohm's laws. The transmission/reflection processes of electrons through the conductor excite the electromagnetic modes of the environment, rendering the scattering inelastic, and reducing the current at low voltage, an effect called environmental Coulomb blockade [1]. This picture, valid in the limit of a weak conductance, changes in the opposite limit of a good conductance [2]. The description of tunnelling via discrete charge states becomes then ill defined, raising the question of whether dynamic Coulomb blockade (DCB) survives or is completely washed out by quantum fluctuations. It is quite clear that DCB vanishes for a perfectly transmitting conductor. This property is shared by shot noise which results as well from the random current pulses due to tunneling events. Such similarity was concretized [3, 4] through a challenging relationship between the DCB reduction of the current in a one-channel conductor in series with a weak impedance and the noise without impedance (see Fig.(1)). More generally, the DCB variation of the n-1th cumulant of the current was related to the n-th cumulant without environment [5,6]. The environmental effect on the third cumulant has been the subject of a recent intensive experimental and theoretical activity [6,7].An ohmic environment could as well simulate the electronic interactions in the coherent conductor [8]. In this view, one can wonder whether a one channel conductor in series with a resistance is equivalent to a one dimensional interacting system, described by the TLL model [9]. This is already suggested by the power law behavior at small transmission with an exponent determined by r = e 2 R/h, the dimensionless environmental resistance, instead of the microscopic interaction parameter [1]. Furthermore, Kindermann and Nazarov [10] have shown recently that at low enough energy, a many-channel conductor in series with a weak resistance r ≪ 1 behaves as a one-channel conductor with an effective energy dependent transmission T (E, r) similar to that obtained in a weakly interacting one-dimensional wire in the presence of a backscattering center [11]. In this framework, the variation of the current due to DCB is rather given by the shot noise computed through T (E, r) instead of the bare transmission T .In this Letter we fully extend the analogy to a TLL in order to explore the case of an arbitrary resistance r in series with a coherent one channel cond...
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