Noncommutative Electrodynamics with covariant coordinates

We study Noncommutative Electrodynamics using the concept of covariant coordinates. We propose a scheme for interpreting the formalism and construct two basic examples, a constant field and a plane wave. Superposing these two, we find a modification of the dispersion relation. Our results differ from those obtained via the Seiberg-Witten map.Comment: 5 pages, published versio

Particle-hole symmetry in a sandpile model

In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similar to particle avalanches. A combined particle-hole sandpile model is then defined where particle avalanches are created with probability $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.Comment: Four pages, our figure

Janus Black Holes

In this paper Janus black holes in AdS3 are considered. These are static solutions of an Einstein-scalar system with broken translation symmetry along the horizon. These solutions are dual to interface conformal field theories at finite temperature. An approximate solution is first constructed using perturbation theory around a planar BTZ black hole. Numerical and exact solutions valid for all sets of parameters are then found and compared. Using the exact solution the thermodynamics of the system is analyzed. The entropy associated with the Janus black hole is calculated and it is found that the entropy of the black Janus is the sum of the undeformed black hole entropy and the entanglement entropy associated with the defect.Comment: 28 pages, 2 figures, reference adde

Exact equqations and scaling relations for f-avalanche in the Bak-Sneppen evolution model

Infinite hierarchy of exact equations are derived for the newly-observed f-avalanche in the Bak-Sneppen evolution model. By solving the first order exact equation, we found that the critical exponent which governs the divergence of the average avalanche size, is exactly 1 (for all dimensions), confirmed by the simulations. Solution of the gap equation yields another universal exponent, denoting the the relaxation to the attractor, is exactly 1. We also establish some scaling relations among the critical exponents of the new avalanche.Comment: 5 pages, 1 figur

Chaos in Sandpile Models

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.Comment: 5 pages, 6 figure

Symplectic Reduction and Symmetry Algebra in Boundary Chern-Simons theory

We derive the Kac-Moody algebra and Virasoro algebra in Chern-Simons theory with boundary by using the symplectic reduction method and the Noether procedures.Comment: References are adde

Critical States in a Dissipative Sandpile Model

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included

Holographic View of Causality and Locality via Branes in AdS/CFT Correspondence

We study dynamical aspects of holographic correspondence between d=5 anti-de Sitter supergravity and $d=4$ super Yang-Mills theory. We probe causality and locality of ambient spacetime from super Yang-Mills theory by studying transmission of low-energy brane waves via an open string stretched between two D3-branes in Coulomb branch. By analyzing two relevant physical threshold scales, we find that causality and locality is encoded in the super Yang-Mills theory provided infinite tower of long supermultiplet operators are added. Massive W-boson and dual magnetic monopole behave more properly as extended, bilocal objects. We also study causal time-delay of low-energy excitation on heavy quark or meson and find an excellent agreement between anti-de Sitter supergravity and super Yang-Mills theory descriptions. We observe that strong `t Hooft coupling dynamics and holographic scale-size relation thereof play a crucial role to the agreement of dynamical processes

Sandpile avalanche dynamics on scale-free networks

Avalanche dynamics is an indispensable feature of complex systems. Here we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent $\gamma$ through the Bak-Tang-Wiesenfeld (BTW) sandpile model. The threshold height of a node $i$ is set as $k_i^{1-\eta}$ with $0\leq\eta<1$, where $k_i$ is the degree of node $i$. Using the branching process approach, we obtain the avalanche size and the duration distribution of sand toppling, which follow power-laws with exponents $\tau$ and $\delta$, respectively. They are given as $\tau=(\gamma-2 \eta)/(\gamma-1-\eta)$ and $\delta=(\gamma-1-\eta)/(\gamma-2)$ for $\gamma<3-\eta$, 3/2 and 2 for $\gamma>3-\eta$, respectively. The power-law distributions are modified by a logarithmic correction at $\gamma=3-\eta$.Comment: 8 pages, elsart styl

Seiberg-Witten Transforms of Noncommutative Solitons

We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the commutative variables. This gives a precise identification of the moduli of these solutions as locations of branes. On the other hand, an instanton solution in four dimensions allows deformation away from the projection operator construction. We evaluate the Seiberg-Witten transform of the U(2) instanton and show that it has a finite size determined by the noncommutative scale and by the deformation parameter \rho. For large \rho, the profile of the D0-brane density of the instanton agrees surprisingly well with that of the BPST instanton on commutative space.Comment: 29 pages, LaTeX; comments added, typos corrected, and a reference added; comments added, typos correcte