The zero-energy bound states at the edges or vortex cores of chiral p-wave superconductors should behave like Majorana fermions. We introduce a model Hamiltonian that describes the tunnelling process when electrons are injected into such states. Using a non-equilibrium Green function formalism, we find exact analytic expressions for the tunnelling current and noise and identify experimental signatures of the Majorana nature of the bound states to be found in the shot noise. We discuss the results in the context of different candidate materials that support triplet superconductivity. Experimental verification of the Majorana character of midgap states would have important implications for the prospects of topological quantum computation.

We explore the use of exact diagonalization methods for solving the self-consistent equations of the cellular dynamical mean field theory for the one-dimensional regular and extended Hubbard models. We investigate the nature of the Mott transition and convergence of the method as a function of cluster size as well as the optimal allocation of computational resources between bath and ''cluster-impurity'' sites, with a view to develop a renormalization group method in higher dimensions. We assess the performance of the method by comparing results for the Green's functions in both the spin density wave and charge density wave phases with accurate density matrix renormalization group ͑DMRG͒ calculations.

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.

We present an implementation of a continuous matrix product state for two-component fermions in one-dimension. We propose a construction of variational matrices with an efficient parameterization that respects the translational symmetry of the problem (without being overly constraining) and readily meets the regularity conditions that arise from removing the ultraviolet divergences in the kinetic energy. We test the validity of our approach on an interacting spin-1/2 system and observe that the ansatz correctly predicts the ground state magnetic properties for the attractive spin-1/2 Fermi gas, including the phase-oscillating pair correlation function in the partially polarized regime.Comment: 6 pages, 5 figure