A novel realization of the Calogero-Moser scattering states as coherent states

A novel realization is provided for the scattering states of the $N$-particle Calogero-Moser Hamiltonian. They are explicitly shown to be the coherent states of the singular oscillators of the Calogero-Sutherland model. Our algebraic treatment is straightforwardly extendable to a large number of few and many-body interacting systems in one and higher dimensions.Comment: 9 pages, REVTe

An explicit realization of fractional statistics in one dimension

An explicit realization of anyons is provided, using the three-body Calogero model. The fact that in the coupling domain, $-1/4<g<0$, the angular spectrum can have a band structure, leads to the manifestation of the desired phase in the wave function, under the exchange of the paticles. Concurrently, the momentum corresponding to the angular variable is quantized, exactly akin to the relative angular momentum quantization in two dimensional anyonic systemComment: 12 page

Achievements and prospects of genomics-assisted breeding in three legume crops of the semi-arid tropics

Advances in next-generation sequencing and genotyping technologies have enabled generation of large-scale genomic resources such as molecular markers, transcript reads and BAC-end sequences (BESs) in chickpea, pigeonpea and groundnut, three major legume crops of the semi-arid tropics. Comprehensive transcriptome assemblies and genome sequences have either been developed or underway in these crops. Based on these resources, dense genetic maps, QTL maps as well as physical maps for these legume species have also been developed. As a result, these crops have graduated from ‘orphan’ or ‘less-studied’ crops to ‘genomic resources rich’ crops. This article summarizes above mentioned advances in genomics and genomics-assisted breeding applications in the form of marker-assisted selection (MAS) for hybrid purity assessment in pigeonpea; marker-assisted backcrossing (MABC) for introgressing QTL region for drought-tolerance related traits, Fusarium wilt (FW) resistance and Ascochyta blight (AB) resistance in chickpea; late leaf spot (LLS), leaf rust and nematode resistance in groundnut. We critically present the case of use of other modern breeding approaches like marker-assisted recurrent selection (MARS) and genomic selection (GS) to utilize the full potential of genomics-assisted breeding for developing superior cultivars with enhanced tolerance to various environmental stresses. In addition, this article recommends the use of advanced- backcross (AB-backcross) breeding and development of specialized populations such as multi-parents advanced generation intercross (MAGIC) for creating new variations that will help developing superior lines with broadened genetic base. In summary, we propose the use of integrated genomics and breeding approach in these legume crops to enhance crop productivity in marginal environments ensuring food security in developing countries

Galaxy Clusters Associated with Short GRBs. II. Predictions for the Rate of Short GRBs in Field and Cluster Early-Type Galaxies

We determine the relative rates of short GRBs in cluster and field early-type galaxies as a function of the age probability distribution of their progenitors, P(\tau) \propto \tau^n. This analysis takes advantage of the difference in the growth of stellar mass in clusters and in the field, which arises from the combined effects of the galaxy stellar mass function, the early-type fraction, and the dependence of star formation history on mass and environment. This approach complements the use of the early- to late-type host galaxy ratio, with the added benefit that the star formation histories of early-type galaxies are simpler than those of late-type galaxies, and any systematic differences between progenitors in early- and late-type galaxies are removed. We find that the ratio varies from R(cluster)/R(field) ~ 0.5 for n = -2 to ~ 3 for n = 2. Current observations indicate a ratio of about 2, corresponding to n ~ 0 - 1. This is similar to the value inferred from the ratio of short GRBs in early- and late-type hosts, but it differs from the value of n ~ -1 for NS binaries in the Milky Way. We stress that this general approach can be easily modified with improved knowledge of the effects of environment and mass on the build-up of stellar mass, as well as the effect of globular clusters on the short GRB rate. It can also be used to assess the age distribution of Type Ia supernova progenitors.Comment: ApJ accepted versio