Spin-Charge Decoupling and Orthofermi Quantum Statistics

Currently Gutzwiller projection technique and nested Bethe ansatz are two main methods used to handle electronic systems in the $U$ infinity limit. We demonstrate that these two approaches describe two distinct physical systems. In the nested Bethe ansatz solutions, there is a decoupling between the spin and charge degrees of freedom. Such a decoupling is absent in the Gutzwiller projection technique. Whereas in the Gutzwiller approach, the usual antisymmetry of space and spin coordinates is maintained, we show that the Bethe ansatz wave function is compatible with a new form of quantum statistics, viz., orthofermi statistics. In this statistics, the wave function is antisymmetric in spatial coordinates alone. This feature ultimately leads to spin-charge decoupling.Comment: 12 pages, LaTex Journal_ref: A slightly abridged version of this paper has appeared as a brief report in Phys. Rev. B, Vol. 63, 132405 (2001

The Role of Components of Demographic Change in Economic Development : Whither the Trend ?

In this paper, we investigate the role of the components of demographic change on economic development. Population growth has both positive and negative effects on income growth. Kelley and Schmidt (1995) states that high birth rates are costly in terms of growth but this effect can be offset by a positive impact of mortality reductions. We study how the weight of each effect has changed over time considering a panel of countries over the last four decades. We find that there is little gain to expect from further reductions in mortality in developing countries, and that the effect of birth rates has become positive in developed countries. In contrast to the earlier study, where growth enhancing effect of population density is felt consistently for all decades, we find that the effect is limited only to the sixties.Demographic components; endogenous growth; panel data

REPRESENTATION-CONSTRAINED CANONICAL CORRELATION-ANALYSIS: A HYBRIDIZATION OF CANONICAL CORRELATION AND PRINCIPAL COMPONENT ANALYSIS

The classical canonical correlation analysis is extremely greedy to maximize the squared correlation between two sets of variables. As a result, if one of the variables in the dataset-1 is very highly correlated with another variable in the dataset-2, the canonical correlation will be very high irrespective of the correlation among the rest of the variables in the two datasets. We intend here to propose an alternative measure of association between two sets of variables that will not permit the greed of a select few variables in the datasets to prevail upon the fellow variables so much as to deprive the latter of contributing to their representative variables or canonical variates. Our proposed Representation-Constrained Canonical correlation (RCCCA) Analysis has the Classical Canonical Correlation Analysis (CCCA) at its one end (t=0) and the Classical Principal Component Analysis (CPCA) at the other (as t tends to be very large). In between it gives us a compromise solution. By a proper choice of t, one can avoid hijacking of the representation issue of two datasets by a lone couple of highly correlated variables across those datasets. This advantage of the RCCCA over the CCCA deserves a serious attention by the researchers using statistical tools for data analysis.Representation, constrained, canonical, correlation, principal components, variates, global optimization, particle swarm, ordinal variables, computer program, FORTRAN versus detection.

Site-Specific Colloidal Crystal Nucleation by Template-enhanced Particle Transport

The monomer surface mobility is the single most important parameter that decides the nucleation density and morphology of islands during thin film growth. During template-assisted surface growth in particular, low surface mobilities can prevent monomers from reaching target sites and this results in a partial to complete loss of nucleation control. While in atomic systems a broad range of surface mobilities can be readily accessed, for colloids, owing to their large size, this window is substantially narrow and therefore imposes severe restrictions in extending template-assisted growth techniques to steer their self-assembly. Here, we circumvented this fundamental limitation by designing templates with spatially varying feature sizes, in this case moire patterns, which in the presence of short-range depletion attraction presented surface energy gradients for the diffusing colloids. The templates serve a dual purpose, first, directing the particles to target sites by enhancing their surface mean free paths and second, dictating the size and symmetry of the growing crystallites. Using optical microscopy, we directly followed the nucleation and growth kinetics of colloidal islands on these surfaces at the single-particle level. We demonstrate nucleation control, with high fidelity, in a regime that has remained unaccessed in theoretical, numerical and experimental studies on atoms and molecules as well. Our findings pave the way for fabricating non-trivial surface architectures composed of complex colloids and nanoparticles.Comment: 12 pages, 3 figure