Decorated star-triangle relations and exact integrability of the one-dimensional Hubbard model

The exact integrability of the one-dimensional Hubbard model is demonstrated with the help of a novel set of triangle relations, the decorated star-triangle relations. The covering two-dimensional statistical mechanical model obeys the star-triangle or Yang-Baxter relation. A conjecture is presented for the eigenvalues of the transfer matrix.     

Estimates of the number of quantal bound states in one and three dimensions

Using the relation between the number of bound states and the number of zeros of the radial eigen-functionψ(r), or equivalently, that ofφ(r)=rψ(r) in the range 0⩽r⩽∞, the upper bounds on the number of bound states generated by potentialV(r) in different angular momentum channels are obtained in three dimension. Using a similar procedure, the upper bound on the number of bound states in one dimension is also deduced. The analysis is restricted to a class of potentials for whichE=0 is the threshold. By taking a number of specific examples, it is demonstrated that both in one and three dimensions, the estimate of the upper bound obtained by this procedure is very close to or equal to the exact number of bound states. The correlation of the present method with the Levison’s theorem and WKB approximation is discussed.     

Kinetic studies on the mechanism of the relative catalytic activities of surfactants in the oxidation of amino-acids by chloramine-T

The kinetics of oxidation of amino-acids by chloramine-T in the presence of two different surfactants (cationic and anionic surfactants) in acidic medium has been studied. The kinetic results show that the reaction is fractional and first order with respect to substrate and oxidant respectively. The influence of halides, ionic strength and solvent on the rate has been studied. The effect of surfactants on the reaction show that the reaction velocity is highly sensitive to the variation of surfactant concentration. The micelle-substrate binding constant (K) and co-operativity index have been calculated indicating the stability of the catalyst substrate micelles (complex) so formed. A probable reaction path has been suggested and discussed in the light of various experimental results and findings.     

Quantum dot bio-conjugate: as a western blot probe for highly sensitive detection of cellular proteins

In the present study, we report a quantum dot (QD)-tailored western blot analysis for a sensitive, rapid and flexible detection of the nuclear and cytoplasmic proteins. Highly luminescent CdTe and (CdTe)ZnS QDs are synthesized by aqueous method. High resolution transmission electron microscopy, Raman spectroscopy, fourier transform infrared spectroscopy, fluorescence spectroscopy and X-ray diffraction are used to characterize the properties of the quantum dots. The QDs are functionalized with antibodies of prostate apoptosis response-4 (Par-4), poly(ADP-ribose) polymerases and β actin to specifically bind with the proteins localized in the nucleus and cytoplasm of the cells, respectively. The QD-conjugated antibodies are used to overcome the limitations of conventional western blot technique. The sensitivity and rapidity of protein detection in QD-based approach is very high, with detection limits up to 10 pg of protein. In addition, these labels provide the capability of enhanced identification and localization of marker proteins in intact cells by confocal laser scanning microscopy.     

Quasi-bound states, resonance tunnelling, and tunnelling times generated by twin symmetric barriers

In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit-Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit-Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.     

Regionwise absorption in nuclear optical model

A mathematical procedure to calculate the contribution to the reaction cross-section from a shell of radiusr and thickness Δ around the scattering centre within the frame work of a nuclear optical model is presented. The method is illustrated by describing graphically the regionwise absorption in nucleon-nucleus and nucleus-nucleus optical scattering. It is demonstrated that unlike in nucleon-nucleus scattering, in the nucleus-nucleus scattering volume absorptive optical potential, in general, does not imply that absorption is taking place in the entire nuclear volume; it is confined to mostly the surface region.     

The Heisenberg ferromagnet in spin coherent state representation

A new approach to Heisenberg ferromagnet using the spin coherent state representation is developed. The differential operator representation of spin angular momentum operators is used to derive thec-number analogs of the basic quantum mechanical equations, viz., the Schrödinger, Bloch and Liouville equations for the Heisenberg ferromagnet. As an important illustration of our formulation, which has noad hoc assumptions and does not use any boson representation, the excitation spectrum for one, two and three spin waves is obtained. In these cases it is also shown that eigenvalue spectrum can be obtained by completely ignoring the kinematical interactions.