One-dimensional Ginzburg–Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg–Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order α wit...

The statistical correlations between defects in the two-dimensional complex Ginzburg-Landau model are studied in the defect-coarsening regime. In particular the defect-velocity probability distribution is determined and has the same high velocity tail found for the purely dissipative time-dependent Ginzburg-Landau (TDGL) model. The spiral arms of the defects lead to a very different behavior fo...

Motivated by recent developments in the computation of periods for string compactifications with c = 9, we develop a complementary method which also produces a convenient basis for related calculations. The models are realized as Calabi-Yau hypersurfaces in weighted projective spaces of dimension four or as Landau-Ginzburg vacua. The calculation reproduces known results and also allows a treatm...

The current voltage characteristic of the narrow superconducting channel is investigated by direct numerical integration of the time-dependent Ginzburg Landau equations. We have demonstrated that the steps in the current voltage characteristic correspond to a number of di erent bifurcation points of the time-dependent Ginzburg Landau equations. We have analytically estimated the period and the ...

A new description is proposed for the low-field critical behavior of type-II superconductors. The starting point is the Ginzburg-Landau theory in presence of an external magnetic field H. A set of fictitious vortex variables and a singular gauge transformation are used to rewrite a finite H Ginzburg-Landau functional in terms of a complex scalar field of zero average vorticity. The continuum li...

We consider D-branes wrapped around supersymmetric cycles of Calabi-Yau manifolds from the viewpoint of N = 2 Landau-Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau-Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardy’s procedur...

We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general r...

We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for κ = λ/ξ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-...

We define and investigate deformed n-Calabi-Yau completions of homologically smooth differential graded (=dg) categories. Important examples are: deformed preprojective algebras of connected non Dynkin quivers, Ginzburg dg algebras associated to quivers with potentials and dg categories associated to the category of coherent sheaves on the canonical bundle of a smooth variety. We show that defo...

This paper presents an introduction to phase transitions and critical phenomena on the one hand, and nonequilibrium patterns on the other, using the Ginzburg-Landau theory as a unified language. In the first part, meanfield theory is presented, for both statics and dynamics, and its validity tested self-consistently. As is well known, the mean-field approximation breaks down below four spatial ...