Non-Abelian Tensor Multiplet Equations from Twistor Space

We establish a Penrose-Ward transform yielding a bijection between holomorphic principal 2-bundles over a twistor space and non-Abelian self-dual tensor fields on six-dimensional flat space-time. Extending the twistor space to supertwistor space, we derive sets of manifestly N=(1,0) and N=(2,0) supersymmetric non-Abelian constraint equations containing the tensor multiplet. We also demonstrate how this construction leads to constraint equations for non-Abelian supersymmetric self-dual strings.Comment: v3: 23 pages, revised version published in Commun. Math. Phy

Chern-Simons Solitons, Chiral Model, and (affine) Toda Model on Noncommutative Space

We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons gauge theory coupled to a nonrelativistic complex adjoint matter on noncommutative space. Soliton configurations of this model are related the solutions of the chiral model on noncommutative plane. A generalized Uhlenbeck's uniton method for the chiral model on noncommutative space provides explicit Chern-Simons solitons. Fundamental solitons in the U(1) gauge theory are shaped as rings of charge `n' and spin `n' where the Chern-Simons level `n' should be an integer upon quantization. Toda and Liouville models are generalized to noncommutative plane and the solutions are provided by the uniton method. We also define affine Toda and sine-Gordon models on noncommutative plane. Finally the first order moduli space dynamics of Chern-Simons solitons is shown to be trivial.Comment: latex, JHEP style, 23 pages, no figur

Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations

We describe an infinite-dimensional algebra of hidden symmetries of N=4 supersymmetric Yang-Mills (SYM) theory. Our derivation is based on a generalization of the supertwistor correspondence. Using the latter, we construct an infinite sequence of flows on the solution space of the N=4 SYM equations. The dependence of the SYM fields on the parameters along the flows can be recovered by solving the equations of the hierarchy. We embed the N=4 SYM equations in the infinite system of the hierarchy equations and show that this SYM hierarchy is associated with an infinite set of graded symmetries recursively generated from supertranslations. Presumably, the existence of such nonlocal symmetries underlies the observed integrable structures in quantum N=4 SYM theory.Comment: 24 page

A Connection between Twistors and Superstring Sigma Models on Coset Superspaces

We consider superstring sigma models that are based on coset superspaces G/H in which H arises as the fixed point set of an order-4 automorphism of G. We show by means of twistor theory that the corresponding first-order system, consisting of the Maurer-Cartan equations and the equations of motion, arises from a dimensional reduction of some generalised self-dual Yang-Mills equations in eight dimensions. Such a relationship might help shed light on the explicit construction of solutions to the superstring equations including their hidden symmetry structures and thus on the properties of their gauge theory duals.Comment: v3: 16 pages, typos fixed and minor clarifications adde

Electron Spin Relaxation in a Semiconductor Quantum Well

A fully microscopic theory of electron spin relaxation by the D'yakonov-Perel' type spin-orbit coupling is developed for a semiconductor quantum well with a magnetic field applied in the growth direction of the well. We derive the Bloch equations for an electron spin in the well and define microscopic expressions for the spin relaxation times. The dependencies of the electron spin relaxation rate on the lowest quantum well subband energy, magnetic field and temperature are analyzed.Comment: Revised version as will appear in Physical Review

A search for ferromagnetism in transition-metal-doped piezoelectric ZnO

We present the results of a computational study of ZnO in the presence of Co and Mn substitutional impurities. The goal of our work is to identify potential ferromagnetic ground states within the (Zn,Co)O or (Zn,Mn)O material systems that are also good candidates for piezoelectricity. We find that, in contrast to previous results, robust ferromagnetism is not obtained by substitution of Co or Mn on the Zn site, unless additional carriers (holes) are also incorporated. We propose a practical scheme for achieving such $p$-type doping in ZnO

Equivalence of conservation laws and equivalence of potential systems

We study conservation laws and potential symmetries of (systems of) differential equations applying equivalence relations generated by point transformations between the equations. A Fokker-Planck equation and the Burgers equation are considered as examples. Using reducibility of them to the one-dimensional linear heat equation, we construct complete hierarchies of local and potential conservation laws for them and describe, in some sense, all their potential symmetries. Known results on the subject are interpreted in the proposed framework. This paper is an extended comment on the paper of J.-q. Mei and H.-q. Zhang [Internat. J. Theoret. Phys., 2006, in press].Comment: 10 page

Scattering of Noncommutative Waves and Solitons in a Supersymmetric Chiral Model in 2+1 Dimensions

Interactions of noncommutative waves and solitons in 2+1 dimensions can be analyzed exactly for a supersymmetric and integrable U(n) chiral model extending the Ward model. Using the Moyal-deformed dressing method in an antichiral superspace, we construct explicit time-dependent solutions of its noncommutative field equations by iteratively solving linear equations. The approach is illustrated by presenting scattering configurations for two noncommutative U(2) plane waves and for two noncommutative U(2) solitons as well as by producing a noncommutative U(1) two-soliton bound state.Comment: 1+13 pages; v2: reference added, version published in JHE

The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio

Kinetics and Jamming Coverage in a Random Sequential Adsorption of Polymer Chains

Using a highly efficient Monte Carlo algorithm, we are able to study the growth of coverage in a random sequential adsorption (RSA) of self-avoiding walk (SAW) chains for up to 10^{12} time steps on a square lattice. For the first time, the true jamming coverage (theta_J) is found to decay with the chain length (N) with a power-law theta_J propto N^{-0.1}. The growth of the coverage to its jamming limit can be described by a power-law, theta(t) approx theta_J -c/t^y with an effective exponent y which depends on the chain length, i.e., y = 0.50 for N=4 to y = 0.07 for N=30 with y -> 0 in the asymptotic limit N -> infinity.Comment: RevTeX, 5 pages inclduing figure