Haldane Exclusion Statistics and the Boltzmann Equation

We generalize the collision term in the one-dimensional Boltzmann-Nordheim transport equation for quasiparticles that obey the Haldane exclusion statistics. For the equilibrium situation, this leads to the ``golden rule'' factor for quantum transitions. As an application of this, we calculate the density response function of a one-dimensional electron gas in a periodic potential, assuming that the particle-hole excitations are quasiparticles obeying the new statistics. We also calculate the relaxation time of a nuclear spin in a metal using the modified golden rule.Comment: version accepted for publication in J. of Stat. Phy

Chromium uptake by Fenugreek

Fenugreek (Trigonella foenum- graecum) is both herb (leaves) and a spice (seed) belonging to the family Fabaceae. Fenugreek leaves and seeds are used in the cuisine of India. Fenugreek also has medicinal value. Fenugreek seeds are known to reduce serum glucose and improve glucose tolerance and hence are prescribed to diabetic patients. In the recent past supplemental Chromium is being prescribed to diabetic patients to activate (increased- insulin binding, insulin receptor number, insulin receptor phosphorylation) insulin. Plants can uptake substantial quantities of toxic metals from contaminated soils if these soils are well ameliorated. 

It is then probable that the medicinal efficacy of Fenugreek in the case of diabetes could be enhanced if it takes up chromium from the soil. Preliminary studies are being conducted to note the chromium uptake by Fenugreek from soils which are applied with potassium dichromate

Studies on the Accumulation of Chromium in Fenugreek

Studying Cr uptake by Fenugreek, we note that the maximum concentration of Cr takes place in the shells of the pods followed by leaves, stems and seeds in that order. Interestingly, applied higher doses of Cr does not increase accumulation of Cr in the stems, rather Cr content in the stems levels off. However, the maximum dispersal/distribution of Cr taken up is in the leaves

Classical Dynamics of Anyons and the Quantum Spectrum

In this paper we show that (a) all the known exact solutions of the problem of N-anyons in oscillator potential precisely arise from the collective degrees of freedom, (b) the system is pseudo-integrable ala Richens and Berry. We conclude that the exact solutions are trivial thermodynamically as well as dynamically.Comment: 19 pages, ReVTeX, IMSc/93/0

Magnetic anomalies of offshore Krishna-Godavari basin, eastern continental margin of India

The marine magnetic data acquired from offshore Krishna-Godavari (K-G) basin, eastern continental margin of India (ECMI), brought out a prominent NE-SW trending feature, which could be explained by a buried structural high formed by volcanic activity. The magnetic anomaly feature is also associated with a distinct negative gravity anomaly similar to the one associated with 85°E Ridge. The gravity low could be attributed to a flexure at the Moho boundary, which could in turn be filled with the volcanic material. Inversion of the magnetic and gravity anomalies was also carried out to establish the similarity of anomalies of the two geological features (structural high on the margin and the 85°E Ridge) and their interpretations. In both cases, the magnetic anomalies were caused dominantly by the magnetization contrast between the volcanic material and the surrounding oceanic crust, whereas the low gravity anomalies are by the flexures of the order of 3-4 km at Moho boundary beneath them. The analysis suggests that both structural high present in offshore Krishna-Godavari basin and the 85°E Ridge have been emplaced on relatively older oceanic crust by a common volcanic process, but at discrete times, and that several of the gravity lows in the Bay of Bengal can be attributed to flexures on the Moho, each created due to the load of volcanic material

Gentile statistics and restricted partitions

In a recent paper (Tran et al, Ann. Phys.311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for the restricted or coloured partitions pks (n), which is the number of partitions of an integer n into the summand of sth powers of integers such that each power of a given integer may occur utmost k times. While the method is not rigorous, it reproduces the well-known asymptotic results for s = 1 apart from yielding more general results for arbitrary values of s

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.Comment: 10 pages (TeX), 2 figures available upon reques