WZW-Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson Sigma model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting "WZW-Poisson" manifold M is characterized by a bivector Pi and by a closed three-form H such that [Pi,Pi]_Schouten = .Comment: 4 pages; v2: a reference adde

A direct proof of Kim's identities

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like $1 - q^{\sqrt{n}}$ and $1 - q^{n^2}$, instead of $1 - q^n$. We show here that there is a fourth relation that naturally completes the set, in much the same way that there are four relations for the four elliptic theta functions. We derive all of them directly by proving and using a specialization of Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics

Linear and multiplicative 2-forms

We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac manifolds.Comment: to appear in Letters in Mathematical Physic

Locating Boosted Kerr and Schwarzschild Apparent Horizons

We describe a finite-difference method for locating apparent horizons and illustrate its capabilities on boosted Kerr and Schwarzschild black holes. Our model spacetime is given by the Kerr-Schild metric. We apply a Lorentz boost to this spacetime metric and then carry out a 3+1 decomposition. The result is a slicing of Kerr/Schwarzschild in which the black hole is propagated and Lorentz contracted. We show that our method can locate distorted apparent horizons efficiently and accurately.Comment: Submitted to Physical Review D. 12 pages and 22 figure

A sigma model field theoretic realization of Hitchin's generalized complex geometry

We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin--Vilkovisky classical master equation. Further, the (twisted) classical Batalin--Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology.Comment: 28 pages, Plain TeX, no figures, requires AMS font files AMSSYM.DEF and amssym.tex. Typos in eq. 6.19 and some spelling correcte

Energy minimization using Sobolev gradients: application to phase separation and ordering

A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg-Landau models commonly used in pattern formation and ordering processes.Comment: To appear J. Computational Physic

Exact Solutions of a Model for Granular Avalanches

We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced: Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, velocities of the active region and of the sandpile profile.Comment: 7 pages, 2 figure

Transverse and longitudinal momentum spectra of fermions produced in strong SU(2) fields

We study the transverse and longitudinal momentum spectra of fermions produced in a strong, time-dependent non-Abelian SU(2) field. Different time-dependent field strengths are introduced. The momentum spectra are calculated for the produced fermion pairs in a kinetic model. The obtained spectra are similar to the Abelian case, and they display exponential or polynomial behaviour at high p_T, depending on the given time dependence. We investigated different color initial conditions and discuss the recognized scaling properties for both Abelian and SU(2) cases.Comment: 10 pages, 11 figures; version accepted to PR

Nodal domains on quantum graphs

We consider the real eigenfunctions of the Schr\"odinger operator on graphs, and count their nodal domains. The number of nodal domains fluctuates within an interval whose size equals the number of bonds $B$. For well connected graphs, with incommensurate bond lengths, the distribution of the number of nodal domains in the interval mentioned above approaches a Gaussian distribution in the limit when the number of vertices is large. The approach to this limit is not simple, and we discuss it in detail. At the same time we define a random wave model for graphs, and compare the predictions of this model with analytic and numerical computations.Comment: 19 pages, uses IOP journal style file

Exact solution for random walks on the triangular lattice with absorbing boundaries

The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.Comment: 10 pages, Latex, IOP macro