Related papers: Gradient estimates for the conductivity problem wi…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
We analyze the high-temperature conductivity in one-dimensional integrable models of interacting fermions: the t-V model (anisotropic Heisenberg spin chain) and the Hubbard model, at half-filling in the regime corresponding to insulating…
We consider the behaviour of a critical system in the presence of a gradient perturbation of the couplings. In the direction of the gradient an interface region separates the ordered phase from the disordered one. We develop a scaling…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…
This work establishes novel optimum mixing bounds for the Glauber dynamics on the Hard-core and Ising models. These bounds are expressed in terms of the local connective constant of the underlying graph $G$. This is a notion of effective…
In this work we exploit the integrability of the two-lead Anderson model to compute transport properties of a quantum dot, in and out of equilibrium. Our method combines the properties of integrable scattering together with a…
We develop an Effective Medium Theory to study the electrical transport properties of disordered graphene. The theory includes non-linear screening and exchange-correlation effects allowing us to consider experimentally relevant strengths…
The space charge limited emission of ions from a target in the focus of an intense relativistic electron beam is studied analytically for the case of a spatially varying target density profile. In particular, the emission in the presence of…
The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of…
We present an exact analysis of two conductor-insulator transitions in the random graph model. The average connectivity is related to the concentration of impurities. The adjacency matrix of a large random graph is used as a hopping…
We obtain a novel bound state spectrum of the low energy excitations near the Fermi points of graphene in the presence of a charge impurity. The effects of possible short range interactions induced by the impurity are modelled by suitable…
Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium transfer rates of the boundary sine-Gordon and the…
In this work, we show that the widely used bounce-back boundary condition is an incomplete form of the diffuse reflection boundary condition at the continuum limit for lattice Boltzmann simulations. By utilizing this fact, we can force the…
In this paper, we present a Spectral-Galerkin Method to approximate the zero-index transmission eigenvalues with a conductive boundary condition. This is a new eigenvalue problem derived from the scalar inverse scattering problem for an…
A multi-scale characterization of the field concentrations inside composite and polycrystalline media is developed. The analysis focuses on gradient fields associated with the intensive quantities given by the temperature and the electric…
In part II we constructed the lower bound, in the spirit of $\Gamma$- $\liminf$ for some general classes of singular perturbation problems, with or without the prescribed differential constraint, taking the form E_\e(v):=\int_\Omega…
The problem of blow up of solutions to the initial boundary value problem for non-autonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions of blow up in a…
We generalize the Blonder-Tinkham-Klapwijk theory considering non-diagonal boundary conditions in the Bogoliubov-de Gennes scattering problem, to describe anomalous conductance features often reported for normal-metal/superconductor…
We discuss the initial boundary value problem for a heat equation in a domain surrounded by a layer. The main features of this problem are twofold: on one hand, the layer is thin compared to the scale of the domain, and on the other hand,…
We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is…