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

Relationship Between the Energy Eigenstates of Calogero-Sutherland Models With Oscillator and Coulomb-like Potentials

We establish a simple algebraic relationship between the energy eigenstates of the rational Calogero-Sutherland model with harmonic oscillator and Coulomb-like potentials. We show that there is an underlying SU(1,1) algebra in both of these models which plays a crucial role in such an identification. Further, we show that our analysis is in fact valid for any many-particle system in arbitrary dimensions whose potential term (apart from the oscillator or the Coulomb-like potential) is a homogeneous function of coordinates of degree -2. The explicit coordinate transformation which maps the Coulomb-like problem to the oscillator one has also been determined in some specific cases.Comment: 23 pages, RevTeX, no figure, some clarifications added, version to appear in Journal of Physics

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