Dobrushin states in the \phi^4_1 model

We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic free energy cost, as the length of the interval diverges, of shifting the interface from the midpoint. We then discuss the effect of thermal fluctuations by analyzing the \phi^4_1-measure with Dobrushin boundary conditions. In particular, we obtain a nontrivial limit in a suitable scaling in which the length of the interval diverges and the temperature vanishes. The limiting state is not translation invariant and describes a localized interface. This result can be seen as the probabilistic counterpart of the variational convergence of the associated excess free energy.Comment: 34 page

Chiral d+is superconducting state in the two dimensional t-t' Hubbard model

Applying the recently developed variational approach to Kohn-Luttinger superconductivity to the t-t' Hubbard model in two dimensions, we have found, for sizeable next-nearest neighbor hopping, an electron density controlled quantum phase transition between a d-wave superconducting state close to half filling and an s-wave superconductor at lower electron density. The transition occurs via an intermediate time reversal breaking d+is superconducting phase, which is characterized by nonvanishing chirality and density-current correlation. Our results suggest the possibility of a bulk time reversal symmetry breaking state in overdoped cuprates

Theory of Magneto--Acoustic Transport in Modulated Quantum Hall Systems Near ν=1/2\nu=1/2

Motivated by the experimental results of Willett et al [Phys.Rev. Lett., {\bf 78}, 4478 (1997)] we develop a magneto-transport theory for the response of a two dimensional electron gas (2DEG) in the Fractional Quantum Hall Regime near Landau level filling factor $\nu = 1/2$ to the surface acoustic wave (SAW) in the presence of an added periodic density modulation. We assume there exists a Composite Fermion Fermi Surface (CF-FS) at $\nu = 1/2$, and we show that the deformation of the (CF-FS) due to the density modulation can be at the origin of the observed transport anomalies for the experimental conditions. Our analysis is carried out particularly for the non-local case which corresponds to the SAW experiments. We introduce a new model of a deformed CF-FS. The model permits us to explain anomalous features of the response of the modulated 2DEG to the SAW near $\nu = 1/2:$ namely the nonlinear wave vector dependence of the electron conductivity, the appearance of peaks in the SAW velocity shift and attenuation and the anisotropy of the effect, all of which originate from contributions to the conductivity tensor due to the regions of the CF-FS which are flattened by the applied modulation.Comment: 13 pages, 4 figures, the published versio

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions

We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance $\sigma_Y^2$ of the local conductivity. Using perturbation expansions up to third order and fourth order in $\sigma_Y^2$ obtained from the moment equation approach, we construct the general functional dependence of the transport variables in the regime where $\sigma_Y^2$ is of order 1 and larger than 1. Comparison with available numerical simulations give encouraging results and show that the proposed method provides significant improvements over available expansions.Comment: Latex, 14 pages + 5 ps figure

Abelian Magnetic Monopole Dominance in Quark Confinement

We prove Abelian magnetic monopole dominance in the string tension of QCD. Abelian and monopole dominance in low energy physics of QCD has been confirmed for various quantities by recent Monte Carlo simulations of lattice gauge theory. In order to prove this dominance, we use the reformulation of continuum Yang-Mills theory in the maximal Abelian gauge as a deformation of a topological field theory of magnetic monopoles, which was proposed in the previous article by the author. This reformulation provides an efficient way for incorporating the magnetic monopole configuration as a topological non-trivial configuration in the functional integral. We derive a version of the non-Abelian Stokes theorem and use it to estimate the expectation value of the Wilson loop. This clearly exhibits the role played by the magnetic monopole as an origin of the Berry phase in the calculation of the Wilson loop in the manifestly gauge invariant manner. We show that the string tension derived from the diagonal (abelian) Wilson loop in the topological field theory (studied in the previous article) converges to that of the full non-Abelian Wilson loop in the limit of large Wilson loop. Therefore, within the above reformulation of QCD, this result (together with the previous result) completes the proof of quark confinement in QCD based on the criterion of the area law of the full non-Abelian Wilson loop.Comment: 33 pages, Latex, no figures, version accepted for publication in Phys. Rev. D (additions of sec. 4.5 and references, and minor changes

Interplay between edge states and simple bulk defects in graphene nanoribbons

We study the interplay between the edge states and a single impurity in a zigzag graphene nanoribbon. We use tight-binding exact diagonalization techniques, as well as density functional theory calculations to obtain the eigenvalue spectrum, the eigenfunctions, as well the dependence of the local density of states (LDOS) on energy and position. We note that roughly half of the unperturbed eigenstates in the spectrum of the finite-size ribbon hybridize with the impurity state, and the corresponding eigenvalues are shifted with respect to their unperturbed values. The maximum shift and hybridization occur for a state whose energy is inverse proportional to the impurity potential; this energy is that of the impurity peak in the DOS spectrum. We find that the interference between the impurity and the edge gives rise to peculiar modifications of the LDOS of the nanoribbon, in particular to oscillations of the edge LDOS. These effects depend on the size of the system, and decay with the distance between the edge and the impurity.Comment: 10 pages, 15 figures, revtex