Properties of 1D transport strongly depend on the proper choice of boundary conditions. It has been frequently stated that the Luttinger Liquid (LL) conductance is renormalized by the interaction as g e 2 h . To contest this result I develop a model of 1D LL wire with the interaction switching off at the infinities. Its solution shows that there is no renormalization of the universal conductance while the electrons have a free behavior in the source and drain reservoirs.

The ground state of a phase-coherent mesoscopic system is sensitive to its environment. We investigate the persistent current of a ring with a quantum dot which is capacitively coupled to an external circuit with a dissipative impedance. At zero temperature, zero-point quantum fluctuations lead to a strong suppression of the persistent current with decreasing external impedance. We emphasize the role of displacement currents in the dynamical fluctuations of the persistent current and show that with decreasing external impedance the fluctuations exceed the average persistent current.

We consider tunneling between two edges of Quantum Hall liquids (QHL) of filling factors ν0,1 = 1/(2m0,1 +1), with m0 ≥ m1 ≥ 0, through two point contacts forming Mach-Zehnder interferometer. Quasiparticle description of the interferometer is derived explicitly through the instanton duality transformation of the initial electron model. For m0 +m1 +1 ≡ m > 1, tunneling of quasiparticles of charge e/m leads to non-trivial m-state dynamics of effective flux through the interferometer, which restores the regular "electron" periodicity of the current in flux. The exact solution available for equal propagation times between the contacts of interferometer shows that the interference pattern depends in this case on voltage and temperature only through a common amplitude. The main qualitative elements of our approach can be summarized as follows. The phase difference between the two point contacts expressed in terms of the effective flux Φ through the MZI contains, in addition to the external flux Φ ex , a statistical contribution. This contribution emerges, since each electron coherently tunneling at different contacts changes Φ by ±mΦ 0 , where m = m 0 + m 1 + 1 and Φ 0 is the flux quantum. As a result, the system has m quantum states which differ by number of flux quanta modulo m which are not mixed * also at St. Petersburg State Polytechnical University, Center for Advanced Studies, St. Petersburg 195251, Russia. by perturbative electron tunneling. However, in the nonperturbative regime of strong tunneling, the states are mixed as Φ is changed by ±Φ 0 by tunneling of individual quasiparticles. This implies that the quasiparticles have to carry the charge e/m and coincide with the quasiparticles e * = 2eν 0 ν 1 /(ν 0 +ν 1 ) = e/m in one point contact [6]. (Flux dynamics in the MZI is similar to that in the antidot tunneling [7], where, however, m = m 0 − m 1 , and the e/m quasiparticles are different from those in individual contacts.) The quasiparticle Lagrangian for MZI derived below is a mathematical expression of the flux-induced electron-quasiparticle transmutation. If the times t 0 and t 1 of propagation between the contacts along the two edges of the interferometer are equal: ∆t ≡ t 0 − t 1 = 0, the quasiparticle Lagrangian can be solved by methods of the exactly solvable models. The resultant expression for the tunneling current shows the crossover from the quasiparticle tunneling at large voltages to the electron tunneling at low voltages. Our results correct Ref. 2 by showing that the quasiparticle model used in that work does not correspond in the weak-tunneling limit to electron tunneling at two separate point contacts, and also restrict the validity of the quasiparticle current found in [3] to the leading term in the large-V asymptotics.In details, we start with the electronic model of MZI (Fig.

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We have analyzed Coulomb drag between currents of interacting electrons in two parallel one-dimensional conductors of finite length L attached to external reservoirs. For strong coupling, the relative fluctuations of electron density in the conductors acquire energy gap M. At energies larger than gamma = constxv(-)exp(-LM/v(-))/L+gamma(+), where gamma(+) is the impurity scattering rate, and, for L>v(-)/M, where v(-) is the fluctuation velocity, the gap leads to an "ideal" drag with almost equal currents in the conductors. At low energies the drag is suppressed by coherent instanton tunneling, and the zero-temperature transconductance vanishes, indicating the Fermi-liquid behavior.