arXiv subjects

A. Shukla

Publications and source records attributed to A. Shukla.

At least 55 records · Page 3Linked to original sources

arXiv2014

General N = 2 Supersymmetric Quantum Mechanical Model: Supervariable Approach to its Off-Shell Nilpotent Symmetries

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0 + 1)-dimensional N = 2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θand \barθwith θ^2 = \barθ^2 = 0, θ\barθ+ \barθθ= 0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N = 2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations.

hep-th↗

arXiv2014

Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory

Taking the simple examples of an Abelian 1-form gauge theory in two (1 + 1)-dimensions, a 2-form gauge theory in four (3 + 1)-dimensions and a 3-form gauge theory in six (5 + 1)-dimensions of spacetime, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p (p = 1, 2, 3,...) dimensions of spacetime. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5 + 1)-dimensions of spacetime, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field theory.

hep-th↗

arXiv2014

Electron Correlations and Two-Photon States in Polycyclic Aromatic Hydrocarbon Molecules: A Peculiar Role of Geometry

We present numerical studies of one- and two-photon excited states ordering in a number of polycyclic aromatic hydrocarbon molecules: coronene, hexa-peri-hexabenzocoronene and circumcoronene, all possessing $D_{6h}$ point group symmetry versus ovalene with $D_{2h}$ symmetry, within the Pariser-Parr-Pople model of interacting $π$-electrons. The calculated energies of the two-photon states as well as their relative two-photon absorption cross-sections within the interacting model are qualitatively different from single-particle descriptions. More remarkably, a peculiar role of molecular geometry is found. The consequence of electron correlations is far stronger for ovalene, where the lowest spin-singlet two-photon state is a quantum superposition of pairs of lowest spin triplet states, as in the linear polyenes. The same is not true for $D_{6h}$ group hydrocarbons. Our work indicates significant covalent character, in valence bond language, of the ground state, the lowest spin triplet state and a few of the lowest two-photon states in $D_{2h}$ ovalene but not in those with $D_{6h}$ symmetry.

cond-mat.str-el↗

arXiv2014

Subgap Two-Photon States in Polycyclic Aromatic Hydrocarbons: Evidence for Strong Electron Correlations

Strong electron correlation effects in the photophysics of quasi-one-dimensional $π$-conjugated organic systems such as polyenes, polyacetylenes, polydiacetylenes, etc., have been extensively studied. Far less is known on correlation effects in two-dimensional $π$-conjugated systems. Here we present theoretical and experimental evidence for moderate repulsive electron-electron interactions in a number of finite polycyclic aromatic hydrocarbon molecules with $D_{6h}$ symmetry. We show that the excited state orderings in these molecules are reversed relative to that expected within one-electron and mean-field theories. Our results reflect similarities as well as differences in the role and magnitude of electron correlation effects in these two-dimensional molecules compared to those in polyenes.

cond-mat.str-el↗

arXiv2013

Analysis of the 3DVAR Filter for the Partially Observed Lorenz '63 Model

The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and the objective is to estimate the system state in an on-line fashion; this situation arises, for example, in weather forecasting. The sequential particle filter is then impractical and ad hoc filters, which employ some form of Gaussian approximation, are widely used. Prototypical of these ad hoc filters is the 3DVAR method. The goal of this paper is to analyze the 3DVAR method, using the Lorenz '63 model to exemplify the key ideas. The situation where the data is partial and noisy is studied, and both discrete time and continuous time data streams are considered. The theory demonstrates how the widely used technique of variance inflation acts to stabilize the filter, and hence leads to asymptotic accuracy.

math.DS↗

arXiv2013

Curci-Ferrari Type Condition in Hamiltonian Formalism: A Free Spinning Relativistic Particle

The Curci-Ferrari (CF)-type of restriction emerges in the description of a free spinning relativistic particle within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism when the off-shell nilpotent and absolutely anticommuting (anti-)BRST symmetry transformations for this system are derived from the application of horizontality condition (HC) and its supersymmetric generalization (SUSY-HC) within the framework of superfield formalism. We show that the above CF-condition, which turns out to be the secondary constraint of our present theory, remains time-evolution invariant within the framework of Hamiltonian formalism. This time-evolution invariance (i) physically justifies the imposition of the (anti-)BRST invariant CF-type condition on this system, and (ii) mathematically implies the linear independence of BRST and anti-BRST symmetries of our present theory.

hep-th↗

arXiv2012

Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimensional supermanifold parameterized by an even (bosonic) variable (τ) and a pair of odd (fermionic) variables θand \barθ(with θ^2 = \barθ^2 = 0,\; θ\barθ+ \barθθ= 0) of the Grassmann algebra. One of the most important features of our present investigation is the derivation of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST symmetry transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system.

hep-th↗

arXiv2012

K-edge X-ray absorption spectra in transition metal oxides beyond the single particle approximation: shake-up many body effects

The near edge structure (XANES) in K-edge X-ray absorption spectroscopy (XAS) is a widely used tool for studying electronic and local structure in materials. The precise interpretation of these spectra with the help of calculations is hence of prime importance, especially for the study of correlated materials which have a complicated electronic structure per se. The single particle approach, for example, has generally limited itself to the dominant dipolar cross-section. It has long been known however that effects beyond this approach should be taken into account, both due to the inadequacy of such calculations when compared to experiment and the presence of shake-up many-body satellites in core-level photoemission spectra of correlated materials. This effect should manifest itself in XANES spectra and the question is firstly how to account for it theoretically and secondly how to verify it experimentally. By using state-of-the-art first principles electronic structure calculations and 1s photoemission measurements we demonstrate that shake-up many-body effects are present in K-edge XAS dipolar spectra of NiO, CoO and CuO at all energy scales. We show that shake-up effects can be included in K-edge XAS spectra in a simple way by convoluting the single-particle first-principles calculations including core-hole effects with the 1s photoemission spectra. We thus describe all features appearing in the XAS dipolar cross-section of NiO and CoO and obtain a dramatic improvement with respect to the single-particle calculation in CuO. These materials being prototype correlated magnetic oxides, our work points to the presence of shake-up effects in K-edge XANES of most correlated transition metal compounds and shows how to account for them, paving the way to a precise understanding of their electronic structure.

cond-mat.mtrl-sci↗

arXiv2012

Dual-BRST symmetry: 6D Abelian 3-form gauge theory

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5 + 1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.

hep-th↗

arXiv2012

Multiwavelength study of TeV Blazar Mrk421 during giant flare

Context: The nearby (z=0.031) TeV blazar Mrk421 was reported to be in a high state of flux activity since November, 2009. Aims: To investigate possible changes in the physical parameters of Mrk421 during its high state of activity using multiwavelength data. Methods: We have observed this source in bright state using High Altitude GAmma Ray (HAGAR) telescope array at energies above 250 GeV during February 13 - 19, 2010. Optical, X-ray and gamma-ray archival data are also used to obtain the SEDs and light curves. Results: Mrk421 was found to undergo one of its brightest flaring episodes on February 17, 2010 by various observations in X-rays and gamma-rays. HAGAR observations during February 13 - 19, 2010 at the energies above 250 GeV show an enhancement in the flux level, with a maximum flux of ~ 7 Crab units being detected on February 17, 2010. We present the spectral energy distributions during this flaring episode and investigate the correlation of the variability in X-ray and gamma-ray bands. Conclusions: Our multiwavelength study suggests that the flare detected during February 16 and 17, 2010 could arise due to a passing shock in the jet.

astro-ph.HE↗

arXiv2011

Comments on the dual-BRST symmetry

In view of a raging controversy on the topic of dual-Becchi-Rouet-Stora-Tyutin (dual-BRST/co-BRST) and anti-co-BRST symmetry transformations in the context of four (3+1)-dimensional (4D) Abelian 2-form and 2D (non-)Abelian 1-form gauge theories, we attempt, in our present short note, to settle the dust by taking the help of mathematics of differential geometry, connected with the Hodge theory, which was the original motivation for the nomenclature of "dual-BRST symmetry" in our earlier set of works. It has been claimed, in a recent set of papers, that the co-BRST symmetries are not independent of the BRST symmetries. We show that the BRST and co-BRST symmetries are independent symmetries in the same fashion as the exterior and co-exterior derivatives are independent entities belonging to the set of de Rham cohomological operators of differential geometry.

hep-th↗

arXiv2011

Multiwavelength study of TeV Blazar Mrk421 during giant flare and observations of TeV AGNs with HAGAR

The radiation mechanism of very high energy $γ$-ray emission from blazars and crucial parameters like magnetic field, and size of the emitting region are not well understood yet. To understand the above mentioned properties of blazars, we observed five nearby TeV $γ$-ray emitting blazars (Mrk421, Mrk501, 1ES2344+514, 1ES1218+304 and 3C454.3) and one radio galaxy (M87) using the High Altitude GAmma Ray (HAGAR) telescope. HAGAR is an array of seven telescopes located at Hanle, India to detect Cherenkov light caused by extensive air showers initiated by $γ$-rays. Mrk421 was observed to undergo one of its brightest flaring episodes on 2010 February 17, and detected by various experiments in X-rays and $γ$- rays. HAGAR observations of this source during 2010 February 13 - 19, in the energies above 250 GeV show an enhancement in the flux level, with a flux of 6-7 Crab units being detected on 2010 February 17. We present the spectral energy distribution of the source during this flaring episode. In addition to this, the analysis procedure to extract $γ$-ray signal from HAGAR data is discussed and preliminary results on all the AGNs are presented.

astro-ph.HE↗

arXiv2011

Topologically massive non-Abelian theory: superfield formalism

We apply the well-established techniques of geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism in the context of four (3 + 1)-dimensional (4D) dynamical non-Abelian 2-form gauge theory by exploiting its inherent "scalar" and "vector" gauge symmetry transformations and derive the corresponding off-shell nilpotent and absolutely anticommuting BRST and anti-BRST symmetry transformations. Our approach leads to the derivation of three (anti-) BRST invariant Curci-Ferrari (CF)-type restrictions that are found to be responsible for the absolute anticommutativity of the BRST and anti-BRST symmetry transformations. We derive the coupled Lagrangian densities that respect the (anti-) BRST symmetry transformations corresponding to the "vector" gauge transformations. We also capture the (anti-) BRST invariance of the CF-type restrictions and coupled Lagrangian densities within the framework of our superfield approach. We obtain, furthermore, the off-shell nilpotent (anti-) BRST symmetry transformations when the (anti-) BRST symmetry transformations corresponding to the "scalar" and "vector" gauge symmetries are merged together. These off-shell nilpotent "merged" (anti-) BRST symmetries are, however, found to be not absolutely anticommuting in nature.

hep-th↗

arXiv2011

Oxygen disorder in ice probed by X-ray Compton scattering

We use electron momentum density in ice as a tool to quantify order-disorder transitions by comparing Compton profiles differences of ice VI, VII, VIII and XII with respect to ice Ih. Quantitative agreement is found between theory and experiment for ice VIII, which is the most ordered phase. Robust signatures of the oxygen disorder are identified in the momentum density for the VIII-VII ice phase transition. The unique aspect of this work is the determination of the fraction n_e of electron directly involved in phase transitions as well as the use of position space signatures for quantifying oxygen site disorder.

cond-mat.mtrl-sci↗

arXiv2010

Multiple pre-edge structures in Cu K-edge of high Tc cuprates revealed by high resolution x-ray absorption spectroscopy

Using high resolution x-ray absorption spectroscopy and state-of-the-art electronic structure calculations we demonstrate that the pre-edge region at the Cu K-edge of high T$_c$ cuprates is composed of several excitationsinvisible in standard X-ray absorption spectra. We consider in detail the case of Ca$_{2-x}$CuO$_2$Cl$_2$ and show that the many pre-edge excitations (two for c-axis polarization, four for in-plane polarization and out-of-plane incident X-ray momentum) are dominated by off-site transitions and intersite hybridization. This demonstrates the relevance of approaches beyond the single-site model for the description of the pre-edges of correlated materials. Finally, we show the occurrence of a doubling of the main edge peak that is most visible when the polarization is along the c-axis. This doubling, that has not been seen in any previous absorption data in cuprates, is not reproduced by first principles calculations. We suggest that this peak is due to many-body charge-transfer excitations, while all the other visible far-edge structures are single particle in origin. Our work indicates that previous interpretations of the Cu K-edge X-ray absorption spectra in high T$_c$ cuprates can be profitably reconsidered.

cond-mat.mtrl-sci↗

arXiv2010

Fully self-consistent calculations of nuclear Schiff moments

We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely self-consistent odd-nucleus mean-field theory by modifying the Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation, and include the effects of nucleon dipole moments alongside those of a CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg differ significantly from those of previous calculations when the CP-violating interaction is of isovector character.

nucl-th↗

arXiv2009

Deformed shell model results for two neutrino positron double beta decay of $^{74}$Se

Half-lives $T_{1/2}^{2ν}$ for two neutrino positron double beta decay modes $β^{+}$EC/ECEC are calculated for $^{74}$Se, a nucleus of current experimental interest, using deformed shell model based on Hartree-Fock states employing a modified Kuo interaction in ($^{2}p_{3/2}$, $^{1}f_{5/2}$, $^{2}p_{1/2}$, $^{1}g_{9/2}$) space. The calculated half-life for the ECEC mode is $\sim 10^{26}$yr and it may be possible to observe this in the near future with improved sensitivity of experiments.

nucl-th↗

arXiv2009

How the hydrogen bond in NH$_4$F is revealed with Compton scattering

In order to probe electron wave functions involved in the bonding of NH$_4$F, we have performed Compton scattering experiments in an oriented single crystal and in a powder. Ab initio calculations of the Compton profiles for NH$_4$F and NH$_4$Cl are used to enlighten the nature of the bonds in the NH$_4$F crystal. As a consequence, we are able to show significant charge transfer in the ammonium ion which is not observable using other methods. Our study provides a compelling proof for hydrogen bond formation in NH$_4$F.

cond-mat.mtrl-sci↗