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Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearityApr 29 2014Sep 09 2014We address the existence and stability of spatial localized modes supported by a parity-time-symmetric complex potential in the presence of power-law nonlinearity. The analytical expressions of the localized modes, which are Gaussian in nature, are obtained ... More

Supersymmetry generated one-way invisible PT-symmetric optical crystalsJan 20 2014Mar 13 2014We use supersymmetry transformations to design transparent and one-way reflectionless (thus unidirectionally invisible) complex crystals with balanced gain and loss profiles. The scattering coefficients are investigated using the transfer matrix approach. ... More

Some Solvable Quantum Mechanical Models and Their SymmetriesMay 23 2013This thesis is focused on some solvable quantum mechanical models and their associated symmetries.

Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomialsSep 29 2012Mar 12 2013Using an appropriate change of variable, the Schr\"odinger equation is transformed into a second-order differential equation satisfied by recently discovered Jacobi type $X_m$ exceptional orthogonal polynomials. This facilitates the derivation of infinite ... More

A generalized quantum nonlinear oscillatorOct 16 2009We examine various generalizations, e.g. exactly solvable, quasi-exactly solvable and non-Hermitian variants, of a quantum nonlinear oscillator. For all these cases, the same mass function has been used and it has also been shown that the new exactly ... More

Nonlinear localized modes in PT-symmetric optical media with competing gain and lossJun 25 2013Nov 22 2013The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical ... More

Nonlinear localized modes in PT-symmetric Rosen-Morse potential wellApr 08 2013Apr 09 2013We report the existence and properties of localized modes described by nonlinear Schroedinger equation with complex PT-symmetric Rosen-Morse potential well. Exact analytical expressions of the localized modes are found in both one dimensional and two-dimensional ... More

Dirac electron in graphene under supersymmetry generated magnetic fieldsFeb 19 2014Jul 01 2014We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B} = \widetilde{\mathcal{B}}(x,\lambda) \hat{e}_z$ for which the massless Dirac electron possesses exact solution. The inhomogeneity appearing ... More

A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2xApr 19 2010It is shown that the PT symmetric Hamiltonian with the periodic potential V(x) = 4 cos^2 x + 4 i V_0 sin 2x can be mapped into a Hermitian Hamiltonian for $V_0<0.5$, by a similarity transformation. It is also shown that there exist a second critical point ... More

Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillatorJan 05 2011The generalized Swanson Hamiltonian $H_{GS} = w (\tilde{a}\tilde{a}^\dag+ 1/2) + \alpha \tilde{a}^2 + \beta \tilde{a}^{\dag^2}$ with $\tilde{a} = A(x)d/dx + B(x)$, can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity ... More

Coherent state of a nonlinear oscillator and its revival dynamicsOct 31 2009The coherent state of a nonlinear oscillator having a nonlinear spectrum is constructed using Gazeau Klauder formalism. The weighting distribution and the Mandel parameter are studied. Details of the revival structure arising from different time scales ... More

Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomialsMay 26 2012Aug 21 2012Using the method of point canonical transformation, we derive some exactly solvable rationally extended quantum Hamiltonians which are non-Hermitian in nature and whose bound state wave functions are associated with Laguerre- or Jacobi-type $X_1$ exceptional ... More

Nonsingular potentials from excited state factorization of a quantum system with position dependent massAug 20 2011Sep 19 2011The modified factorization technique of a quantum system characterized by position-dependent mass Hamiltonian is presented. It has been shown that the singular superpotential defined in terms of a mass function and a excited state wave function of a given ... More

Rotation of cold molecular ions inside a Bose-Einstein condensateJul 20 2016Oct 13 2016We use recently developed angulon theory [Phys. Rev. Lett. 114, 203001 (2015)] to study the rotational spectrum of a cyanide molecular anion immersed into Bose-Einstein condensates of rubidium and strontium. Based on $\textit {ab initio}$ potential energy ... More

Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schroedinger HamiltoniansOct 07 2009Some exactly solvable potentials in the position dependent mass background are generated whose bound states are given in terms of Laguerre- or Jacobi-type $X_1$ exceptional orthogonal polynomials. These potentials are shown to be shape invariant and isospectral ... More

Continuous supersymmetric transformation for photonic designJan 25 2019We propose to use a continuous supersymmetric (SUSY) transformation of a dielectric permittivity profile in order to design a photonic mode sorter. The iso-spectrality of the SUSY transformation ensures that modes of the waveguide preserve their propagation ... More

Modes and exceptional points in waveguides with impedance boundary conditionsSep 09 2016A planar waveguide with impedance boundary, composed of non-perfect metallic plates, and with passive or active dielectric filling is considered. We show the possibility of selective mode guiding and amplification when homogeneous pump is added to the ... More

Supersymmetric microring laser arraysFeb 08 2019Coherent combination of emission power from an array of coupled semiconductor lasers operating on the same chip is of fundamental and technological importance. In general, the nonlinear competition among the array supermodes can entail incoherence and ... More

Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approachJan 08 2010Feb 10 2010Here we have studied first and second-order intertwining approach to generate isospectral partner potentials of position-dependent (effective) mass Schroedinger equation. The second-order intertwiner is constructed directly by taking it as second order ... More

Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold SupersymmetryApr 04 2012We investigate effect of position-dependent mass profiles on dynamical breaking of N-fold supersymmetry in several type B and type X_2 models. We find that N-fold supersymmetry in rational potentials in the constant-mass background are steady against ... More

On Mathematical Functions for Theoretical and Experimental Distributions for Shrutis (Micro Tonal Intervals) and Their Application in Hindustani MusicFeb 06 2015In this work, exact mathematical functions have been formulated for three important theoretical Shruti (micro tonal interval) distributions, i.e. for Western Compilation, Deval, and Nagoji Row in Hindustani music. A generalized mathematical function for ... More

Supersymmetric inversion of effective-range expansionsJan 16 2015May 26 2015A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e expanded, which ... More

A Study of N-Acetyl aspartic acid/Creatine Ratio in the White Matter of HIV Positive Patients and Its ApplicationFeb 27 2015A total of 50 patients were enrolled in the study, and MRI brain with MR spectroscopy was done. Tuberculosis was the most common neurologic disease found in the HIV positive group, consisting of 9 patients. Seven of these patients had tuberculous meningitis ... More

Finite-size scaling study of dynamic critical phenomena in a vapor-liquid transitionSep 14 2016Via a combination of molecular dynamics (MD) simulations and finite-size scaling (FSS) analysis, we study dynamic critical phenomena for the vapor-liquid transition in a three dimensional Lennard-Jones system. The phase behavior of the model, including ... More

Kinetics of Vapor-Solid Phase Transitions: Structure, growth and mechanismApr 21 2016Kinetics of separation between the low and high density phases in a single component Lennard-Jones model has been studied via molecular dynamics simulations, at a very low temperature, in the space dimension $d=2$. For densities close to the vapor (low ... More

Droplet growth during vapor-liquid transition in a 2D Lennard-Jones fluidSep 14 2016Results for the kinetics of vapor-liquid phase transition have been presented from the molecular dynamics simulations of a single component two-dimensional Lennard-Jones fluid. The phase diagram for the model, primary prerequisite for this purpose, has ... More

Kinetics of Fluid Phase SeparationJan 22 2015We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have been pointed out. ... More

Dimensionality Dependence of Aging in Kinetics of Diffusive Phase Separation: Behavior of order-parameter autocorrelationJan 14 2015Behavior of two-time autocorrelation during the phase separation in solid binary mixtures are studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art ... More

Giant magnetothermal conductivity and magnetostriction effect in charge ordered Nd$_{0.8}$Na$_{0.2}$MnO$_{3}$ compoundMar 23 2015Oct 10 2015We present results on resistivity ($\rho$), magnetization ($M$), thermal conductivity ($\kappa$), magnetostriction ($\frac{\Delta L}{L(0)}$) and specific heat ($C_{p}$) of charge-orbital ordered antiferromagnetic Nd$_{0.8}$Na$_{0.2}$MnO$_{3}$ compound. ... More

Determination of intrinsic ferroelectric polarization in lossy improper ferroelectric systemsSep 07 2016We measured the intrinsic hysteretic polarization in lossy improper and nanoferroelectric systems where the nonhysteretic polarization and leakage are large and the relaxation takes place over a broader time scale. We used different measurement protocols ... More

Field-induced spin-structural transition and giant magnetostriction in Ising chain $α$-CoV$_2$O$_6$May 22 2013Jan 06 2014We have investigated the temperature and magnetic field dependence of magnetization, specific heat ($C_p$), and relative sample length change ($\Delta L/L_0$) for understanding the field-induced spin-structural change in quasi-one-dimensional spin chain ... More

Critical exponents and irreversibility lines of La$_{0.9}$Sr$_{0.1}$CoO$_3$ single crystalJan 17 2013We have studied the dynamic and static critical behavior of spin glass transition in insulating La$_{0.9}$Sr$_{0.1}$CoO$_3$ single crystal by ac susceptibility and dc magnetization measurements in the vicinity of its freezing temperature ($T_f$). The ... More

Giant magnetocaloric effect in magnetically frustrated EuHo$_2$O$_4$ and EuDy$_2$O$_4$ compoundsSep 12 2012We have investigated the magnetic and magnetocaloric properties of EuHo$_2$O$_4$ and EuDy$_2$O$_4$ by magnetization and heat capacity measurements down to 2 K. These compounds undergo a field-induced antiferromagnetic to ferromagnetic transition and exhibit ... More

3d-4f spin interaction induced giant magnetocaloric effect in zircon-type DyCrO4 and HoCrO4 compoundsSep 05 2013We have investigated the influence of 3d-4f spin interaction on magnetic and magnetocaloric properties of DyCrO$_4$ and HoCrO$_4$ compounds by magnetization and heat capacity measurements. Both the compounds exhibit complicated magnetic properties and ... More

On Statistical Analysis of the Pattern of Evolution of Perceived Emotions Induced by Hindustani Music- A Study Based on Listener ResponsesFeb 08 2015The objective of this study is to find the underlying pattern of how perception of emotions has evolved in India. Here Hindustani Music has been used as a reference frame for tracking the changing perception of emotions. It has been found that different ... More

Anisotropic magnetic properties and giant magnetocaloric effect in antiferromagnetic $R$MnO$_3$ crystals ($R$=Dy, Tb, Ho and Yb)Nov 29 2011We have systematically investigated the magnetic properties and magnetocaloric effect (MCE) in $R$MnO$_3$ ($R$$=$Dy, Tb, Ho and Yb) single crystals. Above a critical value of applied field ($H_c$), $R$MnO$_3$ undergo a first-order antiferromagnetic (AFM) ... More

Categorization of Tablas by Wavelet AnalysisJan 03 2016Tabla, a percussion instrument, mainly used to accompany vocalists, instrumentalists and dancers in every style of music from classical to light in India, mainly used for keeping rhythm. This percussion instrument consists of two drums played by two hands, ... More

Griffiths phase in solid-solution of ferromagnetic manganite and cobaltiteSep 06 2011We report the existence of Griffiths phase (GP) over a wide range of $x$ in La$_{0.6}$Sr$_{0.4}$Mn$_{1-x}$Co$_x$O$_3$, the solid solution of ferromagnetic (FM) La$_{0.6}$Sr$_{0.4}$MnO$_3$ and La$_{0.6}$Sr$_{0.4}$CoO$_3$, from magnetization measurements. ... More

Continuously Varying Critical Exponents Beyond Weak UniversalityApr 26 2016We show, from magnetization measurements, that the the critical exponents \beta, \gamma and \delta of the ferromagnetic to paramagnetic transition in [Sm_{1-y}Nd_{y}]_{0.52}[Sr]_{0.48}MnO_3 vary continuously with Nd concentration (y>0.4) and the critical ... More

Large magnetocapacitance in electronic ferroelectric manganite systemsNov 04 2013We have observed a sizable positive magnetocapacitance ($\sim$$5-90\%$) in perovskite Pr$_{0.55}$Ca$_{0.45}$MnO$_3$ and bilayer Pr(Sr$_{0.1}$Ca$_{0.9}$)$_2$Mn$_2$O$_7$ system under 5T magnetic field across 20-100 K below the magnetic transition point ... More

Anomalous thermal expansion of Sb$_2$Te$_3$ topological insulatorJun 30 2012We have investigated the temperature dependence of the linear thermal expansion along the hexagonal c axis ($\Delta L$), in-plane resistivity ($\rho$), and specific heat ($C_p$) of the topological insulator Sb$_2$Te$_3$ single crystal. $\Delta L$ exhibits ... More

Geometrically frustrated GdInO$_3$: An exotic system to study negative thermal expansion and spin-lattice couplingAug 20 2016In this article, we report negative thermal expansion and spin frustration in hexagonal GdInO$_{3}$. Rietveld refinement of the XRD patterns reveal that the negative thermal expansion in the temperature range of 50-100K stems from the triangular lattice ... More

Harmonic and Timbre Analysis of Tabla StrokesOct 15 2015Indian twin drums mainly bayan and dayan (tabla) are the most important percussion instruments in India popularly used for keeping rhythm. It is a twin percussion/drum instrument of which the right hand drum is called dayan and the left hand drum is called ... More

Continuously Varying Critical Exponents Beyond Weak UniversalityApr 26 2016Oct 27 2016Renormalization group theory does not restrict the from of continuous variation of critical exponents which occurs in presence of a marginal operator. However, the continuous variation of critical exponents, observed in different contexts, usually follows ... More

A systematic approach for designing zero-DGD coupled multi-core optical fibersApr 12 2016An analytical method is presented for designing N-coupled multi-core fibers with zero differential group delay. This approach effectively reduces the problem to a system of N-1 algebraic equations involving the associated coupling coefficients and propagation ... More

Study of the properties of Cosmic rays and solar X-Ray Flares by balloon borne experimentsNov 28 2013Indian Centre for Space Physics is engaged in pioneering balloon borne experiments with typical payloads less than ~ 3.5kg. Low cost rubber balloons are used to fly them to a height of about 40km. In a double balloon system, the booster balloon lifts ... More

Large adiabatic temperature and magnetic entropy changes in EuTiO3Aug 17 2015We have investigated the magnetocaloric effect in single and polycrystalline samples of quantum paraelectric EuTiO3 by magnetization and heat capacity measurements. Single crystalline EuTiO3 shows antiferromagnetic ordering due to Eu2+ magnetic moments ... More

Correlation between defect and magnetism of Ar9+ implanted and un-implanted Zn0.95Mn0.05O thin films suitable for electronic applicationJul 18 2013Sol-gel derived thin films of Zn0.95Mn0.05O have been implanted with Ar9+ ions with doses viz. 5x10e14 ions/cm2 (low), 1x10e15 ions/cm2 (intermediate) and 1x10e16 ions/cm2 (high). Structural, morphological, optical and magnetic properties of the films ... More