## Final Activity Report Summary - CONDIMEC (Conductance of disordered mesoscopic conductor obtained from many-body calculation of electronic structure)

In the first year of this project the proposer established his own research group at the Institute of Electrical Engineering of the Slovak Academy of Sciences in accordance with the reintegration goal of the project. The group studied coherent transport of the interacting electron gas in one-dimensional mesoscopic wires and rings. These studies were performed by means of various many-body methods.

Using the Hartree-Fock approximation, we analysed tunnelling of the interacting one-dimensional electron gas through a single impurity positioned in the centre of the one-dimensional wire connected to contacts. We calculated the transmission probability across the impurity and its dependence on the electron energy and wire length. We found results which were in agreement with the results of the so-called Luttinger liquid model. The transmission at the Fermi level decayed asymptotically, like L^(-K), with K depending only on the electron-electron interaction. The result was surprising since the decay was so far believed to be due to the Coulomb correlations, therefore was thought to be absent in the Hartree-Fock approximation.

Moreover, we calculated, using the Hartree-Fock approximation, the persistent current of the interacting one-dimensional electron gas in a mesoscopic one-dimensional ring threaded by magnetic flux. The ring contained a single impurity. We calculated the persistent current as a function of the ring length L, the barrier strength, etc. We found that the persistent current decayed in the limit of large L as L^(-1-K/2). This universal power law was again in agreement with what the previous researchers found in the correlated Luttinger liquid model. These results suggested that the electron-electron interaction in the ring with a single impurity affected the persistent current mainly via the Fock exchange. To further verify this suggestion, we calculated the persistent current of the interacting one-dimensional electrons by means of the quantum Monte Carlo method as well as by means of the exact diagonalisation. Both methods provided a fully correlated many-body solution. Each of them gave us the persistent current decaying with the system length as L^(-1-K/2).

Using the Hartree-Fock approximation, we analysed tunnelling of the interacting one-dimensional electron gas through a single impurity positioned in the centre of the one-dimensional wire connected to contacts. We calculated the transmission probability across the impurity and its dependence on the electron energy and wire length. We found results which were in agreement with the results of the so-called Luttinger liquid model. The transmission at the Fermi level decayed asymptotically, like L^(-K), with K depending only on the electron-electron interaction. The result was surprising since the decay was so far believed to be due to the Coulomb correlations, therefore was thought to be absent in the Hartree-Fock approximation.

Moreover, we calculated, using the Hartree-Fock approximation, the persistent current of the interacting one-dimensional electron gas in a mesoscopic one-dimensional ring threaded by magnetic flux. The ring contained a single impurity. We calculated the persistent current as a function of the ring length L, the barrier strength, etc. We found that the persistent current decayed in the limit of large L as L^(-1-K/2). This universal power law was again in agreement with what the previous researchers found in the correlated Luttinger liquid model. These results suggested that the electron-electron interaction in the ring with a single impurity affected the persistent current mainly via the Fock exchange. To further verify this suggestion, we calculated the persistent current of the interacting one-dimensional electrons by means of the quantum Monte Carlo method as well as by means of the exact diagonalisation. Both methods provided a fully correlated many-body solution. Each of them gave us the persistent current decaying with the system length as L^(-1-K/2).