Quantum percolation in granular metals.

Theory of quantum corrections to conductivity of granular metal films is developed for the realistic case of large randomly distributed tunnel conductances. Quantum fluctuations of intergrain voltages (at energies E much below the bare charging energy scale E(C)) suppress the mean conductance g (E) much more strongly than its standard deviation sigma(E). At sufficiently low energies E(*) any distribution becomes broad, with sigma(E(*)) approximately g (E(*)), leading to strong local fluctuations of the tunneling density of states.

Approximate symmetry laws for percolation in complex systems: Percolation in polydisperse composites.

The concept of so-called global symmetry of percolation models is discussed and extended to multicolored models. An integral equation is obtained, which determines the partial percolation probabilities P(a) for sites of color a. This equation is applied to a polydisperse particulate composite: a mixture of conducting (of relative fraction x(m)) and nonconducting spheres with distributions of sizes n(m)(R) and n(i)(R), respectively.

Topologically protected quantum bits using Josephson junction arrays.

All physical implementations of quantum bits (or qubits, the logical elements in a putative quantum computer) must overcome conflicting requirements: the qubits should be manipulable through external signals, while remaining isolated from their environment. Proposals based on quantum optics emphasize optimal isolation, while those following the solid-state route exploit the variability and scalability of nanoscale fabrication techniques. Recently, various designs using superconducting structures have been successfully tested for quantum coherent operation, however, the ultimate goal of reaching coherent evolution over thousands of elementary operations remains a formidable task.