We compute the Hodge numbers of the polarised (pure) variation of Hodge structure V = grn−1 R f! Z of the Landau-Ginzburg model f : Y → C mirror-dual to a weighted projective space wPn in terms of a variant of Reid’s age function of the anticanonical cone over wPn. This implies, for instance, that wPn has canonical singularities if and only if hn−1,0 V = 1. We state a conjectural formula for th...

Complex Ginzburg-Landau Equations were originated in the theory of Super-conductivity, 13]. When Ginzburg-Landau parameter chosen to be a special constant, the equations are called self-dual vortex equations that were carefully studied by Jaae and Taubes 16]. For the vortex equation on a Riemannian surface , one considers an open, smooth domain with, possibly empty, smooth boundary @. Let L be ...

We search for a Landau–Ginzburg interpretation of non-diagonal modular invariants of tensor products of minimal n = 2 superconformal models, looking in particular at automorphism invariants and at some exceptional cases. For the former we find a simple description as Landau–Ginzburg orbifolds, which reproduce the correct chiral rings as well as the spectra of various Gepner–type models and orbi...

We give a direct proof of the new ”product” expression for the Ramond sector characters of N=2 minimal models recently suggested by E. Witten. Our construction allows us to generalize these expressions to the D and E series of N=2 minimal models, as well as to other N=2 Kazama–Suzuki coset models such as SU(N)×SO(2(N−1))/SU(N−1)×U(1). We verify that these expressions indeed coincide with the co...

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...