Equilibrium configuration of self-gravitating charged dust clouds: Particle approach

A three dimensional Molecular Dynamics (MD) simulation is carried out to explore the equilibrium configurations of charged dust particles. These equilibrium configuration are of astrophysical significance for the conditions of molecular clouds and the interstellar medium. The interaction among the dust grains is modeled by Yukawa repulsion and gravitational attraction. The spherically symmetric equilibria are constructed which are characterized characterized by three parameters: (i) the number of particles in the cloud, (ii) $\Gamma_g$ (defined in the text) where $\Gamma_g^{-1}$ is the short range cutoff of the interparticle potential, and (iii) the temperature of the grains. The effects of these parameters on dust cloud are investigated using radial density profile. The problem of equilibrium is also formulated in the mean field limit where total dust pressure which is the sum of kinetic pressure and electrostatic pressure, balances the self-gravity. The mean field solutions agree well with the results of MD simulations. Astrophysical significance of the results is briefly discussed.Comment: 10 page

Hole and electron dynamics in the triangular-lattice antiferromagnet -- interplay of frustration and spin fluctuations

Single-particle dynamics in the 120$^{\circ}$ ordered antiferromagnetic state of the triangular-lattice Hubbard model is studied using a physically transparent fluctuation approach in terms of multiple magnon emission and absorption processes within the noncrossing approximation. Hole and electron spectral features are evaluated at intermediate $U$, and analyzed in terms of a competition between the frustration-induced direct hopping and the virtual hopping terms. Finite $U$-induced competing interactions and frustration effects contributing through the magnon dispersion are also discussed. Finite contribution to self-energy correction from long-wavelength (Goldstone) modes, together with the high density of electron scattering states in the narrow, sharp peak in the upper band, result in strong fermion-magnon scattering leading to pronounced incoherent behaviour in the electron dynamics. The fluctuation-induced first-order metal-insulator transition due to vanishing band gap is also discussed.Comment: 10 pages, 13 figure

Lawlessness and Economics: Alternative Modes of Governance

How can property rights be protected and contracts be enforced in countries where the rule of law is ineffective or absent? How can firms from advanced market economies do business in such circumstances? In Lawlessness and Economics , Avinash Dixit examines the theory of private institutions that transcend or supplement weak economic governance from the state. In much of the world and through much of history, private mechanisms--such as long-term relationships, arbitration, social networks to disseminate information and norms to impose sanctions, and for-profit enforcement services--have grown up in place of formal, state-governed institutions. Even in countries with strong legal systems, many of these mechanisms continue under the shadow of the law. Numerous case studies and empirical investigations have demonstrated the variety, importance, and merits, and drawbacks of such institutions. This book builds on these studies and constructs a toolkit of theoretical models to analyze them. The models shed new conceptual light on the different modes of governance, and deepen our understanding of the interaction of the alternative institutions with each other and with the government's law. For example, one model explains the limit on the size of social networks and illuminates problems in the transition to more formal legal systems as economies grow beyond this limit. Other models explain why for-profit enforcement is inefficient. The models also help us understand why state law dovetails with some non-state institutions and collides with others. This can help less-developed countries and transition economies devise better processes for the introduction or reform of their formal legal systems.property rights, contracts, law, business, economic governance, private mechanisms, arbitration, social networks, norms, sanctions, reform

Supersymmetry,Shape Invariance and Exactly Solvable Noncentral Potentials

Using the ideas of supersymmetry and shape invariance we show that the eigenvalues and eigenfunctions of a wide class of noncentral potentials can be obtained in a closed form by the operator method. This generalization considerably extends the list of exactly solvable potentials for which the solution can be obtained algebraically in a simple and elegant manner. As an illustration, we discuss in detail the example of the potential $$V(r,\theta,\phi)={\omega^2\over 4}r^2 + {\delta\over r^2}+{C\over r^2 sin^2\theta}+{D\over r^2 cos^2\theta} + {F\over r^2 sin^2\theta sin^2 \alpha\phi} +{G\over r^2 sin^2\theta cos^2\alpha\phi}$$ with 7 parameters.Other algebraically solvable examples are also given.Comment: 16 page