CP_N Solitons in Quantum Hall Systems

We will present here an elementary pedagogical introduction to $CP_N$ solitons in quantum Hall systems. We begin with a brief introduction to both $CP_N$ models and to quantum Hall (QH) physics. Then we focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact $CP_N$ fields for N=1 and N=3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding $CP_N$ field equations. This is followed by a brief summary of our own recent work in this area, done with Sankalpa Ghosh. [ Invited Plenary Lecture at the International Conference on Geometry, Integrability and Nonlinearity in Condensed Matter & Soft Condensed Matter Physics held at Bansko, Bulgaria, July 15-20, 2001. ]Comment: Standard revtex format, 18 pages, no figure

Bimerons in Double Layer Quantum Hall Systems

In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $\nu =1$. Bimerons are excitations corresponding to bound pairs of merons and anti-merons. Bimeron solutions have already been studied at great length by other groups by minimising the microsopic Hamiltonian between microscopic trial wavefunctions. Here we calculate them by numerically solving coupled nonlinear partial differential equations arising from extremisation of the effective action for pseudospin textures. We also calculate the different contributions to the energy of our bimerons, coming from pseudospin stiffness, capacitance and coulomb interactions between the merons. Apart from augmenting earlier results, this allows us to check how good an approximation it is to think of the bimeron as a pair of rigid objects (merons) with logarithmically growing energy, and with electric charge ${1 \over 2}$. Our differential equation approach also allows us to study the dependence of the spin texture as a function of the distance between merons, and the inter layer distance. Lastly, the technical problem of solving coupled nonlinear partial differential equations, subject to the special boundary conditions of bimerons is interesting in its own right.Comment: 8 ps figures included; to be published in IJMP

Solitons in systems of coupled scalar fields

We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential equations that solve the equations of motion when the energy saturates its lower bound. To illustrate the general results, we investigate some systems described by polynomial interactions in the coupled fields.Comment: RevTex4, 5 page

Revenue incentives at the third tier.

Given the poor level of exploitation in most states of even such sources of revenue as have been legislatively assigned to the fiscal domain of panchayati raj institutions, the most important issue is that of incentives for own revenue collection. Incentives can be built into the design of State-local transfers by deducting local revenue potential from closed-ended grant entitlements, thus deeming local collections as having been realised (upto some stipulated fraction of potential if need be). Such a system can work only if the assessment of revenue potential across panchayat jurisdictions is perceived as cross-sectionally fair, and if it carries minimal costs of assessment for the State government. The jurisdiction-specific indicator must also not carry policy endogeneity, with adverse incentives for provision of public services by PRIs. The paper examines these issues and suggests a way by which the revenue potential can be quantified in an operationally useful way, without adverse incentives. The paper also examines whether State governments should be incentivised by the Centre to implement decentralisation and encourage own revenue generation by PRIs.Revenue potential ; Panchayati raj institutions

Noncommutative Gauge Theory, Divergences and Closed Strings

We study the renormalization of non-commutative gauge theories with matter. As in the scalar field theory cases, there are logarithmic infrared divergences resulting from integrating out high momentum modes. In order to reproduce the correct infrared behaviour, the Wilsonian effective action has to include certain ''closed string`` modes with prescribed couplings. In the case of quiver gauge theories, realized in string theory on orbifolds, we identify the required modes with a set of twisted sector fields. These closed string modes have exactly the prescribed couplings to correct the Wilsonian effective action. This provides a concrete origin for the appearance of closed string modes in noncommutative field theories.Comment: 20 pages, 2 figures, LATE