Skyrmions in arbitrarily polarized quantum Hall states

We derive an effective non-linear sigma model for quantum hall systems with arbitrary polarizations, by employing the recently proposed doublet model. We study the topological excitations, in particular, the skyrmions, as a function of the filling fraction as well as the polarization. We determine the relationship between the topological charge density and the electronic charge density, and the statistics of skyrmions. We also estimate the value of spin stiffness by using the dispersion relations that we have obtained recently by employing the time dependent Hartree-Fock approximation for the doublet model. Finally, we point out how the skyrmionic excitations reveal information directly on the number of flux tubes that get attached to the electrons in order to form composite fermions.Comment: 6 page

Quasiprobability distributions in open quantum systems: spin-qubit systems

Quasiprobability distributions (QDs) in open quantum systems are investigated for $SU(2)$, spin like systems, having relevance to quantum optics and information. In this work, effect of both quantum non-demolition (QND) and dissipative open quantum systems, on the evolution of a number of spin QDs are investigated. Specifically, compact analytic expressions for the $W$, $P$, $Q$, and $F$ functions are obtained for some interesting single, two and three qubit states, undergoing general open system evolutions. Further, corresponding QDs are reported for an N qubit Dicke model and a spin-1 system. The existence of nonclassical characteristics are observed in all the systems investigated here. The study leads to a clear understanding of quantum to classical transition in a host of realistic physical scenarios. Variation of the amount of nonclassicality observed in the quantum systems, studied here,are also investigated using nonclassical volume.Comment: 23 pages 13 figure

Analysis Of Shaped Dielectric Lens Array Antenna By Modal expansion

Theradiation pattern of Spheroidal dielectric lens excited by array antennais expressed in terms of spheroidal (SDL) modal expansion. Since the SDL Vector wave functions are not orthogonal, each the SDL modes are expressed in terms of aninfinite sum of Spherical (SPL) vector modes, that exhibit orthogonality over a measurement surface surrounding the lens and array. The spheroidal modal coefficients can be determined by applying boundary condition on the lens surface. Using the determined coefficients near fields on the measurement surface is computed. This field can be easily transformed to the far field using standard modal expansion. This technique has been applied to a 1x2 array at 10 GHz radiating into a SDL lens and the radiated fields computed with 20 SDL modes, with each SDL mode expressed as 20 SPL modes. The results are compared with a well-known EM flow solver

Analysis Shaped Dielectric Lens Antennas using Hybrid method

In this paper hybrid method of analysis of shaped dielectric lens with microstrip patch array is presented. Hybrid method combines the advantage of spherical modal expansion (SME) and geometrical optics (GO). First, SME is used to find the near fields using known far field expressions for the primary source. After obtaining spherical complex modal coefficients (SMCC), each mode is treated as a plane wave radiating through a shaped dielectric lens and analysed using GO. The far field at any point on a spherical surface surrounding the lens is the sum of individual modal contributions, which are then easily transformed to far field using a SME. This hybrid method is independent of lens geometry and computationally faster compared to any electromagnetic simulation software. As expected the prediction accuracy is between that of an exact SME technique and an EM flow solver. Results have been presented for an array with spherical lens

Issues of WTA in shrimp aquaculture for exports and options for way forward

The global trade agreements under the ambit of World Trade Organization(WTO) (hereafter called as WTA), cover goods, services and intellectual property. They spell out the principles of liberalization, and the permitted exceptions. They include individual countries’ commitments to lower customs tariffs and other trade barriers, and to open and keep open services markets. They also set procedures for settling disputes. They prescribe special treatment for developing countries. They require governments to make their trade policies transparent by notifying the WTO about laws in force and measures adopted, and through regular reports by the secretariat on countries’ trade policies. As fisheries is not having the protection as agriculture under WTO regime, un understanding of WTA is important for fisheries professionals. Though WTA is put in place to ensure free trade among nations, many trade barriers are government-induced restrictions on international trade. The barriers can take many forms, including the following: tariffs, non-tariff barriers to trade import licenses, export licenses, import quotas, subsidies, voluntary export restraints, local content requirements, embargo, currency devaluation. Other trade barriers include differences in culture, customs, traditions, laws, language and currency. Most trade barriers work on the same principle: the imposition of some sort of cost on trade that raises the price of the traded products. If two or more nations repeatedly use trade barriers against each other, then a trade war results. Economists generally agree that trade barriers are detrimental and decrease overall economic efficiency, this can be explained by the theory of comparative advantage. In theory, free trade involves the removal of all such barriers, except perhaps those considered necessary for health or national security. In practice, however, even those countries promoting free trade heavily subsidize certain industries, such as agriculture and steel. Trade barriers are often criticized for the effect they have on the developing world. Because rich-country players call most of the shots and set trade policies, goods such as crops that developing countries are best at producing still face high barriers. Trade barriers such as taxes on food imports or subsidies for farmers in developed economies lead to overproduction and dumping on world markets, thus lowering prices and hurting poor-country farmers. Tariffs also tend to be anti-poor, with low rates for raw commodities and high rates for labour-intensive processed goods. The Commitment to Development Index measures the effect that rich country trade policies actually have on the developing world. Another negative aspect of trade barriers is that it would cause a limited choice of products and would therefore force customers to pay higher prices and accept inferior quality. Trade barriers affecting fisheries and shrimp exports from India are discussed hereunder

Relax, no need to round: integrality of clustering formulations

We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for focusing on convex relaxations are: (a) they come with a certificate of optimality, and (b) they are generic tools which are relatively parameter-free, not tailored to specific assumptions over the input. More precisely, we consider the distributional setting where there are $k$ clusters in $\mathbb{R}^m$ and data from each cluster consists of $n$ points sampled from a symmetric distribution within a ball of unit radius. We ask: what is the minimal separation distance between cluster centers needed for convex relaxations to exactly recover these $k$ clusters as the optimal integral solution? For the $k$-median linear programming relaxation we show a tight bound: exact recovery is obtained given arbitrarily small pairwise separation $\epsilon > 0$ between the balls. In other words, the pairwise center separation is $\Delta > 2+\epsilon$. Under the same distributional model, the $k$-means LP relaxation fails to recover such clusters at separation as large as $\Delta = 4$. Yet, if we enforce PSD constraints on the $k$-means LP, we get exact cluster recovery at center separation $\Delta > 2\sqrt2(1+\sqrt{1/m})$. In contrast, common heuristics such as Lloyd's algorithm (a.k.a. the $k$-means algorithm) can fail to recover clusters in this setting; even with arbitrarily large cluster separation, k-means++ with overseeding by any constant factor fails with high probability at exact cluster recovery. To complement the theoretical analysis, we provide an experimental study of the recovery guarantees for these various methods, and discuss several open problems which these experiments suggest.Comment: 30 pages, ITCS 201