Effective action and adiabatic expansions for the 1-D and 2-D hubbard models at half-filling

We analyze here the occurrence of antiferromagnetic (AFM) correlations in the half-filled Hubbard model in one and two space dimensions using a natural fermionic representation of the model and a newly proposed way of implementing the half-filling constraint. We find that our way of implementing the constraint is capable of enforcing it exactly already at the lowest levels of approximation. We discuss how to develop a systematic adiabatic expansion for the model and how Berry's phase contributions arise quite naturally from the adiabatic expansion. At low temperatures and in the continuum limit the model gets mapped onto an O(3) nonlinear sigma model (NLsigma). A topological, Wess-Zumino term is present in the effective action of the ID NLsigma as expected, while no topological terms are present in 2D. Some specific difficulties that arise in connection with the implementation of an adiabatic expansion scheme within a thermodynamic context are also discussed, and we hint at possible solutions.

Probing Single and Bilayer Graphene Field Effect Transistors By Raman Spectroscopy

This article is a review of our work related to Raman studies of single layer and bilayer graphenes as a function Fermi level shift achieved by electrochemically top gating a field effect transistor. Combining the transport and in situ Raman studies of the field effect devices, a quantitative understanding is obtained of the phonon renormalization due to doping of graphene. Results are discussed in the light of time dependent perturbation theory, with electron phonon coupling parameter as an input from the density functional theory. It is seen that phonons near and Gamma and K points of the Brillouin zone are renormalized very differently by doping. Further, Gamma-phonon renormalization is different in bilayer graphene as compared to single layer, originating from their different electronic band structures near the zone boundary K-point. Thus Raman spectroscopy is not only a powerful probe to characterize the number of layers and their quality in a graphene sample, but also to quantitatively evaluate electron phonon coupling required to understand the performance of graphene devices.

Target space of an asymmetric chiral gauged wzw model

It is shown that the asymmetric chiral gauging of the WZW models give rise to consistent string backgrounds. The target space structure of the chiral gauged SL(2,R) WZW model, with the gauging of subgroups SO(1, 1) in the left and U(1) in the right moving sector, is obtained. We then analyze the symmetries of the background and show the presence of a non-trivial isometry in the canonical parametrization of the WZW model. Using these results, the equivalence of the asymmetric models with the symmetric ones is demonstrated.

Supersolid Phase in One-Dimensional Bose-Hubbard Model With Extended Range Interactions: DMRG And Field Theoretic Study at Different Densities

We use the Density Matrix Renormalization Group and the Abelian bosonization method to study the effect of density on quantum phases of one-dimensional extended Bose-Hubbard model. We predict the existence of supersolid phase and also other quantum phases for this system. We have analyzed the role of extended range interaction parameters on solitonic phase near half-filling. We discuss the effects of dimerization in nearest neighbor hopping and interaction as well as next nearest neighbor interaction on the plateau phase at half-filling.

Supersymmetry In The Two-Anyon Problem

We show that the problem of two anyons interacting through a simple harmonic potential or a Coulomb potential is supersymmetric. The supersymmetry operators map a theory described by statistics parameter θ to one described by π+θ. Thus fermions and bosons go into each other, while semions are supersymmetric by themselves. The simple harmonic problem has a Sp(4) symmetry for any value of θ which explains the energy degeneracies.

On the integrability and chaotic behavior of an ecological model

A three-species food chain model is studied analytically as well as numerically. Integrability of the model is studied using Painleve analysis while chaotic behavior is studied using numerical techniques, such as calculation of Lyapunov exponents, plotting the bifurcation diagram and phase plots. We correct and critically comment on the wrong results reported recently on this ecological model, in a paper by Rai [1995].

Spin and charge density waves in the extended Hubbard model: A slave-boson approach

We use the extended Hubbard model to investigate the properties of the charge- and spin-density-wave phases in the presence of a nearest-neighbors repulsion term in the framework of the slave-boson technique. We show that, contrary to Hartree-Fock results, an instablity may occur for sufficiently high values of the Hubbard repulsion, both in the spin- and charge-density-wave phase, which makes the system discontinuously jump to a phase with a smaller or zero wave amplitude. The limits of applicability of our approach are discussed and our results are compared with previous numerical analysis. The phase diagram of the model at half-filling is determined.

Parallel implementation of alternate quadrant interlocking factorisation method on star topology

This paper discusses the parallel implementation of the solution of a set of linear equations using the Alternative Quadrant Interlocking Factorisation Methods (AQIF), on a star topology. Both the AQIF and LU decomposition methods are mapped onto star topology on an IBM SP2 system, with MPI as the internode communicator. Performance parameters such as speedup, efficiency have been obtained through experimental and theoretical means. The studies demonstrate (i) a mismatch of 15% between the theoretical and experimental results, (ii) scalability of the AQIF algorithm, and (iii) faster executing AQIF algorithm.

Survival of the fittest and zero sum games

Competition for available resources is natural amongst coexisting species, and the fittest contenders dominate over the rest in evolution. The. dynamics of this selection is studied using a simple linear model. It has similarities to features of quantum computation, in particular conservation laws leading to destructive interference. Compared to an altruistic scenario, competition introduces instability and eliminates the weaker species in a finite time.

Synthesis of crystallites of carbon nitride in amorphous carbon

We report the successful synthesis of crystalline carbon nitride by chemical vapor deposition of certain nitrogen containing organic precursors. The precursor is heated and the vapors enter the hot deposition zone where they are pyrolysed and deposited in the form of thin films over pretreated substrates. The powder x-ray diffraction analysis shows clear peaks corresponding to the carbon nitride crystals of tetragonal form in addition to a broad hump corresponding to the amorphous nitrogenated carbon. The crystallites size is similar to300Angstrom and the volume fraction of the crystallites is about similar to7%. The optimum conditions of preparation are found out. The Infrared spectra of these samples also suggest the formation of Carbon Nitride crystals. The analysis reconfirms that the material contains crystallites of Carbon Nitride embedded in an amorphous matrix of nitrogenated carbon. Further the material is characterized by C,H,N elemental analysis, EDX and Raman spectra. Since all the above analyses probe the bulk material, the background amorphous matrix in this case, expecting a clear evidence of nanometer sized crystallites from these tests are unlikely. Attempts are being made to increase the yield of these carbon nitride crystallites.

Dynamics of pulsed flow in an elastic tube

Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow in our attempt to specify the location of the haemorrhagic spot, which, if located accurately, could possibly be operated leading to an instant cure. The model we employ for the purpose is basically fluid mechanical in origin and consists of a viscous fluid, pumped by a periodic force and flowing through an elastic tube. The analogy is with that of blood, pumped from the heart and flowing through an artery or vein. Our results, aided by graphical illustrations, match reasonably well with experimental observations.

Health Monitoring Of Composite Structures Based On Acoustic Wave Sensing Using Fiber Optic Sensors

Structural Health Monitoring has gained wide acceptance in the recent past as a means to monitor a structure and provide an early warning of an unsafe condition using real-time data. Utilization of structurally integrated, distributed sensors to monitor the health of a structure through accurate interpretation of sensor signals and real-time data processing can greatly reduce the inspection burden. The rapid improvement of the Fiber Optic Sensor technology for strain, vibration, ultrasonic and acoustic emission measurements in recent times makes it feasible alternative to the traditional strain gauges, PVDF and conventional Piezoelectric sensors used for Non Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Optical fiber-based sensors offer advantages over conventional strain gauges, and PZT devices in terms of size, ease of embedment, immunity from electromagnetic interference (EMI) and potential for multiplexing a number of sensors. The objective of this paper is to demonstrate the acoustic wave sensing using Extrinsic Fabry-Perot Interferometric (EFPI) sensor on a GFRP composite laminates. For this purpose experiments have been carried out initially for strain measurement with Fiber Optic Sensors on GFRP laminates with intentionally introduced holes of different sizes as defects. The results obtained from these experiments are presented in this paper. Numerical modeling has been carried out to obtain the relationship between the defect size and strain.

Vapor pressure and dissociation energy of (In2O)

The vapor pressure of pure liquid indium, and the sum of pressures of (In) and (In2O) species over the condensed phase mixture {In} + , contained in a silica vessel, have been measured by Knudsen effusion and Langmuir free vaporization methods in the temperatue range 600 to 950°C. Mass spectrometric studies reported in the literature show that (In) and (In2O) are the important species in the vapor phase over the {In} + ; mixture. The vapor pressure of (In2O) corresponding to the reaction, deduced from the present measurements is given by the equation, The “apparent evaporation coefficient” for the condensed phase mixture is approximately 0.8. The energy for the dissociation (In2O) molecule into atoms calculated from the above equation is D°0 = 180.0 (± 1.0) kcal mol−1.

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.