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      Volume 83, Issue 1

      July 2014,   pages  1-164

    • General editorial on publication ethics

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    • $g_2$ Algebra and two-dimensional quasiexactly solvable Hamiltonian related to Poschl–Teller potential

      H Panahi H Rahmati

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      In this article, we write the general form of the quasiexactly solvable Hamiltonian of $g_2$ algebra via one special representation in the $x–y$ two-dimensional space. Then, by choosing an appropriate set of coefficients and making a gauge rotation, we show that this Hamiltonian leads to the solvable Poschl–Teller model on an open infinite strip. Finally, we assign $g_2$ hidden algebra to the Poschl–Teller potential and obtain its spectrum by using the representation space of $g_2$ algebra.

    • Lie and Noether symmetries of systems of complex ordinary differential equations and their split systems

      R Naz F M Mahomed

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      The Lie and Noether point symmetry analyses of a 𝑘th-order system of 𝑚 complex ordinary differential equations (ODEs) with 𝑚 dependent variables are performed. The decomposition of complex symmetries of the given system of complex ODEs yields Lie- and Noether-like operators. The system of complex ODEs can be split into $2m$ coupled real partial differential equations (PDEs) and $2m$ Cauchy–Riemann (CR) equations. The classical approach is invoked to compute the symmetries of the $4m$ real PDEs and these are compared with the decomposed Lie- and Noetherlike operators of the system of complex ODEs. It is shown that, in general, the Lie- and Noether-like operators of the system of complex ODEs and the symmetries of the decomposed system of real PDEs are not the same. A similar analysis is carried out for restricted systems of complex ODEs that split into $2m$ coupled real ODEs. We summarize our findings on restricted complex ODEs in two propositions.

    • Multiscale expansions in discrete world

      Ömer Ünsal Filiz Taşcan Mehmet Naci Özer

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      In this paper, we show the attainability of KdV equation from some types of nonlinear Schrödinger equation by using multiscale expansions discretely. The power of this manageable method is confirmed by applying it to two selected nonlinear Schrödinger evolution equations. This approach can also be applied to other nonlinear discrete evolution equations. All the computations have been made with Maple computer packet program.

    • Infinitely-many conservation laws for two (2+1)-dimensional nonlinear evolution equations in fluids

      Yan Jiang Bo Tian Pan Wang Kun Su

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      In this paper, a method that can be used to construct the infinitely-many conservation laws with the Lax pair is generalized from the (1+1)-dimensional nonlinear evolution equations (NLEEs) to the (2+1)-dimensional ones. Besides, we apply that method to the Kadomtsev– Petviashvili (KP) and Davey–Stewartson equations in fluids, and respectively obtain their infinitelymany conservation laws with symbolic computation. Based on that method, we can also construct the infinitely-many conservation laws for other multidimensional NLEEs possessing the Lax pairs, including the cylindrical KP, modified KP and (2+1)-dimensional Gardner equations, in fluids, plasmas, optical fibres and Bose–Einstein condensates.

    • Solutions to the 𝑁-dimensional radial Schrödinger equation for the potential $ar^2 + br − c/r$

      Ramesh Kumar Fakir Chand

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      Approximate solutions to the 𝑁-dimensional radial Schrödinger equation for the potential $ar^2 + br − c/r$ are obtained by employing the formulation described in Ciftci et al, J. Phys. A 43, 415206 (2010). The problem, for some special cases, is solved numerically. Using this analysis, the energy spectra of a two-dimensional two-electron quantum dot (QD) in a magnetic field are also obtained. The results of this study are in good agreement with the other studies.

    • Approximate eigensolutions of Dirac equation for the superposition Hellmann potential under spin and pseudospin symmetries

      M Hamzavi S M Ikhdair

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      The Hellmann potential is simply a superposition of an attractive Coulomb potential $−a/r$ plus a Yukawa potential 𝑏e${}^{−δr} /r$. The generalized parametric Nikiforov–Uvarov (NU) method is used to examine the approximate analytical energy eigenvalues and two-component wave function of the Dirac equation with the Hellmann potential for arbitrary spin-orbit quantum number 𝜅 in the presence of exact spin and pseudospin (p-spin) symmetries. As a particular case, we obtain the energy eigenvalues of the pure Coulomb potential in the non-relativistic limit.

    • Some exact solutions of magnetized viscous model in string cosmology

      C P Singh

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      In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.

    • Anisotropic spheres with Van derWaals-type equation of state

      S Thirukkanesh F C Ragel

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      We study static spherically symmetric space-time to describe relativistic compact objects with anisotropic matter distribution and derive two classes of exact models to the Einstein–Maxwell system with a modified Van derWaals equation of state. We motivate a Van derWaals-type equation of state to physically signify a high-density domain of quark matter, and the generated exact solutions are shown to contain several classes of exact models reported previously that correspond to various physical scenarios. Geometrical analysis shows that the physical quantities are well behaved so that these models may be used to describe anisotropic charged compact spheres.

    • The modified multiple ($G'/G$)-expansion method and its application to Sharma–Tasso–Olver equation

      Zhang Zhe Desheng Li

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      The modified multiple ($G'/G$)-expansion method is proposed in this paper to construct exact solutions of nonlinear evolution equations. The validity and advantage of the proposed method are illustrated by its application to the Sharma–Tasso–Olver equation. As a result, various exact solutions including hyperbolic functions, trigonometric functions and their mixture with parameters are obtained. When some parameters are taken as special values, the known double solitary-like wave solutions are derived from the double hyperbolic function solution. It is shown that the method introduced in this paper has general significance in searching for exact solutions to the nonlinear evolution equations.

    • Design of nanocomposite film-based plasmonic device for gas sensing

      Kaushik Brahmachari Mina Ray

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      Surface plasmon resonance (SPR) is a very efficient tool for chemical and biological sensing in nanotechnology, nanobiotechnology, medicine and environmental monitoring. A theoretical simulation study incorporating the use of admittance loci design methodology in SPR-based sensing device using gold-tungsten trioxide (Au-WO$_{3−x}$) nanocomposite film is reported in this paper. A simple Kretschmann–Raether-type prism-based plasmonic device consisting of a glass prism, Au-WO$_{3−x}$ nanocomposite film and various gas samples is considered. Complex permittivity for both stoichiometric and non-stoichiometric Au-WO$_{3−x}$ nanocomposite films has been used for the simulation of the admittance loci plots, resonance curves and sensitivity curves by considering angular interrogation at a fixed wavelength of 632.8 nm.

    • Microfocussing of synchrotron X-rays using X-ray refractive lens developed at Indus-2 deep X-ray lithography beamline

      V P Dhamgaye M K Tiwari K J S Sawhney G S Lodha

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      X-ray lenses are fabricated in polymethyl methacrylate using deep X-ray lithography beamline of Indus-2. The focussing performance of these lenses is evaluated using Indus-2 and Diamond Light Source Ltd. The process steps for the fabrication of X-ray lenses and microfocussing at 10 keV at moderate and low emittance sources are compared.

    • The effect of laser beam size in a zig-zag collimator on transverse cooling of a krypton atomic beam

      Vivek Singh V B Tiwari S Singh S R Mishra H S Rawat

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      The effect of size of a cooling laser beam in a zig-zag atomic beam collimator on transverse cooling of a krypton atomic beam is investigated. The simulation results show that discreteness in the interaction between the cooling laser beam and atomic beam, arising due to finite size and incidence angle of the cooling laser beam, significantly reduces the value of transverse velocity capture range of the collimator. The experimental observations show the trend similar to that obtained from simulations. Our study can be particularly useful where a small zig-zag collimator is required.

    • Stieltjes electrostatic model interpretation for bound state problems

      K V S Shiv Chaitanya

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      In this paper, it is shown that Stieltjes electrostatic model and quantum Hamilton Jacobi formalism are analogous to each other. This analogy allows the bound state problem to mimic as 𝑛 unit moving imaginary charges $i\hbar$, which are placed in between the two fixed imaginary charges arising due to the classical turning points of the potential. The interaction potential between 𝑛 unit moving imaginary charges $i\hbar$ is given by the logarithm of the wave function. For an exactly solvable potential, this system attains stable equilibrium position at the zeros of the orthogonal polynomials depending upon the interval of the classical turning points.

    • Linear and nonlinear resonance features of an erbium-doped fibre ring laser under cavity-loss modulation

      Aditi Ghosh R Vijaya

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      The continuous-wave output of a single-mode erbium-doped fibre ring laser when subjected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the dynamical study of these resonances shows that the behaviour of the system exhibits features of a nonlinear damped oscillator under harmonic modulation. These nonlinear dynamical features, including harmonic and subharmonic resonances, have been studied experimentally and analysed with the help of a simple time-domain and frequency-domain information obtained from the output of the laser. All the studies are restricted to the modulation frequency lying in a regime near the relaxation oscillation frequency.

    • Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit

      M Ávila

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      The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic corrections in it. If the decoherence times of a quantum dot computer are ∼100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be > 1010. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.

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