Geometry versus Entanglement in Resonating Valence Bond Liquids

We investigate the behavior of bipartite as well as genuine multipartite entanglement of a resonating valence bond state on a ladder. We show that the system possesses significant amounts of bipartite entanglement in the steps of the ladder while no substantial bipartite entanglement is present in the rails. Genuine multipartite entanglement present in the system is negligible. The results are in stark contrast with the entanglement properties of the same state on isotropic lattices in two and higher dimensions, indicating that the geometry of the lattice can have important implications on the quality of quantum information and other tasks that can be performed by using multiparty states on that lattice.Comment: 6 pages, 8 figures, RevTeX

Inflation is the generic feature of phantom field-not the big-rip

A class of solutions for phantom field corresponding to a generalized k-essence lagrangian has been presented, employing a simple method which provides the scope to explore many such. All the solutions having dynamical state parameter are found to touch the magic line w = -1, asymptotically. The solutions with constant equation of state can represent phantom, quitessence or an ordinary scalar field cosmologies depending on the choice of a couple of parameters of the theory. For w approximately equal to -1, quintessence and phantom models are indistinguishable through the Hubble parameter. Finally, inflation rather than big-rip has been found to be the generic feature of phantom cosmology.Comment: 8 pages, 3 figure

Interacting holographic tachyon model of dark energy

We propose a holographic tachyon model of dark energy with interaction between the components of the dark sector. The correspondence between the tachyon field and the holographic dark energy densities allows the reconstruction of the potential and the dynamics of the tachyon scalar field in a flat Friedmann-Robertson-Walker universe. We show that this model can describe the observed accelerated expansion of our universe with a parameter space given by the most recent observational results.Comment: 7 pages, 8 figures, accepted for publication in IJMP

Fundamental Strings in Open String Theory at the Tachyonic Vacuum

We show that the world-volume theory on a D-p-brane at the tachyonic vacuum has solitonic string solutions whose dynamics is governed by the Nambu-Goto action of a string moving in (25+1) dimensional space-time. This provides strong evidence for the conjecture that at this vacuum the full (25+1) dimensional Poincare invariance is restored. We also use this result to argue that the open string field theory at the tachyonic vacuum must contain closed string excitations.Comment: LaTeX file, 16 pages, references and clarification adde

A note on the decay of noncommutative solitons

We propose an ansatz for the equations of motion of the noncommutative model of a tachyonic scalar field interacting with a gauge field, which allows one to find time-dependent solutions describing decaying solitons. These correspond to the collapse of lower dimensional branes obtained through tachyon condensation of unstable brane systems in string theory.Comment: 8 pages, no figures. Extended version, references adde

Optimal bundle formation and pricing of two products with limited stock

Cataloged from PDF version of article.In this study, we consider the stochastic modeling of a retail firm that sells two types of perishable products in a single period not only as independent items but also as a bundle. Our emphasis is on understanding the bundling practices on the inventory and pricing decisions of the firm. One of the issues we address is to decide on the number of bundles to be formed from the initial product inventory levels and the price of the bundle to maximize the expected profit. Product demands follow a Poisson Process with a price dependent rate. Customer reservation prices are assumed to have a joint distribution. We study the impact of reservation price distributions, initial inventory levels, product prices, demand arrival rates and cost of bundling. We observe that the expected profit decreases as the correlation between the reservation prices of two products increases. With negative correlation, bundling cost has a significant impact on the number of bundles formed. When the product prices are low, the retailer sells individual products as well as the bundle (mixed bundling), when they are high, the retailer sells only bundles (pure bundling). The expected profit and the number of bundles offered decrease as the variance of the reservation price distribution increases. For high starting inventory levels, the retailer reduces bundle price and offers more bundles. The number of bundle sales decreases and the number of individual product sales increases when the arrival rate increases since the need for bundling decreases. Impacts of substitutability and complementarity of products are also investigated. The retailer forms more bundles, or charges higher prices for the bundle or both as the products become more complementary and less substitutable. © 2009 Elsevier B.V. All rights reserved

Bundle pricing of inventories with stochastic demand

Cataloged from PDF version of article.We consider a retailer selling a fixed inventory of two perishable products over a finite horizon. Assuming Poisson arrivals and a bivariate reservation price distribution, we determine the optimal product and bundle prices that maximize the expected revenue. Our results indicate that the performances of mixed bundling, pure bundling and unbundled sales strategies heavily depend on the parameters of the demand process and the initial inventory levels. Bundling appears to be most effective with negatively correlated reservation prices and high starting inventory levels. When the starting inventory levels are equal and in excess of average demand, most of the benefits of bundling can be achieved through pure bundling. However, the mixed bundling strategy dominates the other two when the starting inventory levels are not equal. We also observe that an incorrect modeling of the reservation prices may lead to significant losses. The model is extended to allow for price changes during the selling horizon. It is shown that offering price bundles mid-season may be more effective than changing individual product prices. 2008 Elsevier B.V. All rights reserved

On the universality of distribution of ranked cluster masses at critical percolation

The distribution of masses of clusters smaller than the infinite cluster is evaluated at the percolation threshold. The clusters are ranked according to their masses and the distribution $P(M/L^D,r)$ of the scaled masses M for any rank r shows a universal behaviour for different lattice sizes L (D is the fractal dimension). For different ranks however, there is a universal distribution function only in the large rank limit, i.e., $P(M/L^D,r)r^{-y\zeta } \sim g(Mr^y/L^D)$ (y and $\zeta$ are defined in the text), where the universal scaling function g is found to be Gaussian in nature.Comment: 4 pages, to appear in J. Phys.

Dynamics of magnetic modulation of ferrofluid droplets for digital microfluidic applications

Active control of droplet generation in a microfluidic platform attracts interest for development of digital microfluidic devices ranging from biosensors to micro-reactors to point-of-care diagnostic devices. The present paper characterizes, through an unsteady three-dimensional Volume of Fluid (VOF) simulation, the active control of ferrofluid droplet generation in a microfluidic T-junction in presence of a non-uniform magnetic field created by an external magnetic dipole. Two distinctly different positions of the dipole were considered – one upstream of the junction and one downstream. While keeping the ferrofluid flow rate fixed, a parametric variation of the continuous phase capillary number, dipole strength, and dipole position was carried out. Differences in the flow behaviour in terms of dripping or jetting and the droplet characteristics in terms of droplet formation time period and droplet size were studied. The existence of a threshold dipole strength, below which the magnetic force was not able to influence the flow behaviour, was identified. It was also observed that, for dipoles placed upstream of the junction, droplet formation was suppressed at some higher dipole strengths, and this value was found to increase with increasing capillary number. Droplet time period was also found to increase with increasing dipole strength, along with droplet size, i.e. an increase in droplet volume

Statistics of leading digits leads to unification of quantum correlations

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distribution corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as the Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information theoretic measures violate the Benford's law. We quantitatively discuss the violation of the Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.Comment: v1: 11 pages, 5 figures, 2 tables; v2: 11 pages, 6 figures, 2 tables, new results added, extended version of the published pape