Transition from insulating to a non-insulating temperature dependence of the conductivity in granular metals

We consider interaction effects in a granular normal metal at not very low temperatures. Assuming that all weak localization effects are suppressed by the temperature we replace the initial Hamiltonian by a proper functional of phases and study the possibility for a phase transition depending on the tunneling conductance $g$. It is demonstrated for any dimension that, while at small $g$ the conductivity decays with temperature exponentially, its temperature dependence is logarithmic at large $g.$ The formulae obtained are compared with an existing experiment and a good agreement is found.Comment: 9 pages, a mistake is corrected and several formulae adde

Statistics of Wave Functions in Coupled Chaotic Systems

Using the supersymmetry technique, we calculate the joint distribution of local densities of electron wavefunctions in two coupled disordered or chaotic quantum billiards. We find novel spatial correlations that are absent in a single chaotic system. Our exact result can be interpreted for small coupling in terms of the hybridization of eigenstates of the isolated billiards. We show that the presented picture is universal, independent of microscopic details of the coupling.Comment: 4 pages, 2 figures; acknowledgements and references adde

Coulomb effects in granular materials at not very low temperatures

We consider effects of Coulomb interaction in a granular normal metal at not very low temperatures suppressing weak localization effects. In this limit calculations with the initial electron Hamiltonian are reduced to integrations over a phase variable with an effective action, which can be considered as a bosonization for the granular metal. Conditions of the applicability of the effective action are considered in detail and importance of winding numbers for the phase variables is emphasized. Explicit calculations are carried out for the conductivity and the tunneling density of states in the limits of large $g\gg 1$ and small $g\ll 1$ tunnelling conductances. It is demonstrated for any dimension of the array of the grains that at small $g$ the conductivity and the tunnelling density of states decay with temperature exponentially. At large $g$ the conductivity also decays with decreasing the temparature and its temperature dependence is logarithmic independent of dimensionality and presence of a magnetic field. The tunnelling density of states for $g\gg 1$ is anomalous in any dimension but the anomaly is stronger than logarithmic in low dimensions and is similar to that for disordered systems. The formulae derived are compared with existing experiments. The logarithmic behavior of the conductivity at large $g$ obtained in our model can explain numerous experiments on systems with a granular structure including some high $T_{c}$ materials.Comment: 30 page

45.8-Gb/s and 125-Gb/s CP-QPSK/CP-BPSK field trial over installed submarine cable

We show successful transmission of 45.8-Gb/s and 125-Gb/s coherent-detected polarization-multiplexed quadrature phase-shift keying (CP-QPSK) over both 2054 km and 4108 km of 10-Gb/s non-return to zero (NRZ) optimized field-deployed submarine cable. Moreover we report successful transmission of 45.8-Gb/s coherent-detected polarization-multiplexed binary phase-shift keying (CP-BPSK) over 9420 km of legacy submarine fiber. We present single channel transmission results, as well as wavelength-division multiplexed (WDM) transmission results with co-propagating WDM channels placed on a 100-GHz and on a 50-GHz grid, where we optimized the transmission performance by sweeping the launch power and pre-compensation. For 45.8-Gb/s CP-QPSK a margin with respect to the FEC-limit of 1.7 dBQ was obtained after transmitting over a 4108 km distance in a 50-GHz grid WDM configuration. Considering the transmission of 125-Gb/s CP-QPSK over the same distance and with the same channel configuration, a 1.1 dBQ margin was measured, showing the feasibility of a tenfold increase in transmission capacity over legacy submarine fiber. This significantly delays the costly alternative of deploying a new submarine cable. For the transmission of a 45.8-Gb/s CP-BPSK modulated signal on a 50-GHz WDM grid over a 9420 km distance, a margin of 1.2 dBQ with respect to the FEC-limit is reported. This underlines the great robustness of CP-BPSK towards nonlinear fiber impairments and thereby the feasibility to cross trans-oceanic distances with this modulation format