• Volume 77, Issue 6

December 2011,   pages  1023-1203

• Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics

In this paper some exact solutions including soliton solutions for the KdV equation with dual power law nonlinearity and the $K (m, n)$ equation with generalized evolution are obtained using the trial equation method. Also a more general trial equation method is proposed.

• A stepwise planned approach to the solution of Hilbert’s sixth problem. III: Measurements and von Neumann projection/collapse rule

Supmech, the universal mechanics developed in the previous two papers (Dass, arXiv: 0909.4606[math-ph]; 1002:2061[math-ph]), accommodates both quantum and classical mechanics as subdisciplines (a brief outline is included for completeness); this feature facilitates, in a supmechbased treatment of quantum measurements, an unambiguous treatment of the apparatus as a quantum system approximated well by a classical one. Taking explicitly into consideration the fact that observations on the apparatus are made when it has ‘settled down after the measurement interaction’ and are restricted to macroscopically distinguishable pointer readings, the unwanted superpositions of (system + apparatus) states are shown to be suppressed; this provides a genuinely physics-based justiﬁcation for the (traditionally postulated) von Neumann projection/collapse rule. The decoherence mechanism brought into play by the stated observational constraints is free from the objections against the traditional decoherence program.

• Properties of light ﬂavour baryons in hypercentral quark model

The light ﬂavour baryons are studied within the quark model using the hypercentral description of the three-body system. The conﬁnement potential is assumed as hypercentral Coulomb plus power potential (hCPP$_\nu$ ) with power index 𝜈. The masses and magnetic moments of light ﬂavour baryons are computed for different power indices, 𝜈, starting from 0.5 to 1.5. The predicted masses and magnetic moments are found to attain a saturated value with respect to variation in 𝜈 beyond the power index $\nu &gt; 1.0$. Further, we computed transition magnetic moments and radiative decay width of light ﬂavour baryons. The results are in good agreement with the known experimental as well as other theoretical models.

• Quark model for kaon nucleon scattering

Kaon nucleon elastic scattering is studied using chiral $SU(3)$ quark model including antiquarks. Parameters of the present model are essentially based on nucleon–nucleon and nucleon–hyperon interactions. The mass of the scalar meson 𝜎 is taken as 635 MeV. Using this model, the phase shifts of the 𝑆 and 𝑃 partial waves of the kaon nucleon elastic scattering are investigated for isospins 0 and 1. The results of the numerical calculations of different partial waves are in good agreement with experimental data.

• Probing top anomalous couplings at the Tevatron and the Large Hadron Collider

Chromomagnetic and chromoelectric dipole interactions of the top quark are studied in a model-independent framework. Limits are set on the scale of new physics that might lead to such contributions using latest Tevatron measurements of the $t\bar{t}$ cross-section. It is demonstrated that the invariant mass distribution is a sensitive probe. Prospects at the LHC are examined. It is shown that, for unitarized amplitudes, an increase in the LHC energy is of little importance, while the accumulation of luminosity plays a crucial role.

• On the elliptic ﬂow for nearly symmetric collisions and nuclear equation of state

We present the results of elliptic ﬂow for the collision of nearly symmetric nuclei (10Ne20+13Al27, 18Ar40+21Sc45, 30Zn64+28Ni58, 36Kr86+41Nb93) using the quantum molecular dynamics (QMD) model. General features of elliptic ﬂow are investigated with the help of theoretical simulations. The simulations are performed at beam energies between 45 and 105 MeV/nucleon. A signiﬁcant change can be seen from in-plane to out-of-plane elliptic ﬂow of different fragments with incident energy. A comparison with experimental data is also made. Further, we show that elliptic ﬂow for different fragments follows power-law dependence as given by the function $C(A_{\text{tot}})^{\tau}$.

• Canonical form of Nambu–Poisson bracket: A pedestrian approach

In the seventies, Nambu (Phys. Rev. D7, 2405 (1973)) proposed a new approach to classical dynamics based on an 𝑁-dimensional Nambu–Poisson (NP) manifold replacing the primitive even-dimensional Poisson manifold and on $N–1$ Hamiltonians in place of a single Hamiltonian. This approach has had many promoters including Bayen and Flato (Phys. Rev. D11, 3049 (1975)), Mukunda and Sudarshan (Phys. Rev. D13, 2846 (1976)), and Takhtajan (Comm. Math. Phys. 160, 295 (1994)) among others. While Nambu had originally considered $N = 3$, the illustration of his ideas for $N = 4$ and 6 was given by Chatterjee (Lett. Math. Phys. 36, 117 (1996)) who observed that the classical description of dynamical systems having dynamical symmetries is described elegantly by Nambu’s formalism of mechanics. However, his considerations do not quite yield the beautiful canonical form conjectured by Nambu himself for the 𝑁-ary NP bracket. By making a judicious choice for the ‘extra constant of motion’ of namely, 𝛼 and 𝛽, which are the orientation angles in Kepler problem and isotropic harmonic oscillator (HO) respectively, we show that the dynamical systems with dynamical symmetries can be recast in the beautiful form suggested by Nambu. We believe that the techniques used and the theorems suggested by us in this work are of general interest because of their involvement in the transition from Hamiltonian mechanics to Nambu mechanics.

• Spectroscopic properties of $Pr^{3+}$-doped erbiumoxalate crystals

Spectroscopic properties of praseodymium ions-doped erbium oxalate ($Er_2(C_2O_4)_3 \cdot nH_2O$) crystals have been investigated. The crystals were grown by hydro silica gel method under suitable pH conditions and by single diffusion method. The well-grown crystals are bright and transparent. The dark green colour of these crystals changes with the variation of the concentrations of the dopant ions. The absorption spectra have been measured in the region 200–800 nm at room temperature. Judd–Ofelt intensity parameters for f–f transitions of the $Pr^{3+}$ ions have been determined as $\Omega_2 = 166.7$, $\Omega_4 = 1.103$ and $\Omega_6 = 2.898$. Analyses of the absorption spectra also show a possible energy transfer from the host material to the dopant.

• Quantum logic gates using coherent population trapping states

A scheme is proposed for achieving a controlled phase gate using interaction between atomic spin dipoles. Further, the spin states are prepared in coherent population trap states (CPTs), which are robust against perturbations, laser ﬂuctuations etc. We show that one-qubit and two-qubit operations can easily be obtained in this scheme. The scheme is also robust against decoherences due to spontaneous emissions as the CPT states used are dressed states formed out of Zeeman sublevels of ground states of the bare atom. However, certain practical issues are of concern in actually obtaining the scheme, which are also discussed at the end of this paper.

• Negative edge plasma currents in the SINP tokamak

A tokamak plasma discharge having an increase in duration accompanied with enhanced runaway electron ﬂux has been experimentally studied in this paper. The discharges have been obtained by controlling the applied vertical magnetic ﬁeld ($B^{\text{appl}}_v$) to below a critical value. Such discharges have been observed to have ‘negative edge plasma currents’, detected using an internal Rogowskii coil (IRC). We have tried to correlate the runaway behaviour with the negative edge plasma currents and have explained that these observations are a result of beam plasma instabilities.

• Adhesion energy, surface traction and surface tension in liquid xenon

We calculated the adhesion energy, the surface traction and the surface energy of liquid xenon using molecular dynamics (MD) simulation. The value of the adhesion energy for liquid xenon at a reduced density of 0.630 was found to be 0.591 J/m2 and the surface traction has a peak at $z = 3.32 Å$. It was observed that the attraction of the molecules in the liquid surface which produces a resistance to penetration decreases with temperature. This may be attributed to the greater average separation of molecules at higher temperature.

• Schwarzian derivative as a proof of the chaotic behaviour

In recent years, a sufﬁcient condition for determining chaotic behaviours of the nonlinear systems has been characterized by the negative Schwarzian derivative (Hacıbekiroğlu et al, Nonlinear Anal.: Real World Appl. 10, 1270 (2009)). In this work, the Schwarzian derivative has been calculated for investigating the quantum chaotic transition points in the high-temperature superconducting frame of reference, which is known as a nonlinear dynamical system that displays some macroscopic quantum effects. In our previous works, two quantum chaotic transition points of the critical transition temperature, $T_c$, and paramagnetic Meissner transition temperature, $T_{\text{PME}}$, have been phenomenologically predicted for the mercury-based high-temperature superconductors (Onbaşlı et al, Chaos, Solitons and Fractals 42, 1980 (2009); Aslan et al, J. Phys.: Conf. Ser. 153, 012002 (2009); Çataltepe, Superconductor (Sciyo Company, India, 2010)). The $T_c$, at which the one-dimensional global gauge symmetry is spontaneously broken, refers to the second-order phase transition, whereas the $T_{\text{PME}}$, at which time reversal symmetry is broken, indicates the change in the direction of orbital current in the system (Onbaşlı et al, Chaos, Solitons and Fractals 42, 1980 (2009)). In this context, the chaotic behaviour of the mercury-based high-temperature superconductors has been investigated by means of the Schwarzian derivative of the magnetic moment versus temperature. In all calculations, the Schwarzian derivatives have been found to be negative at both $T_c$ and $T_{\text{PME}}$ which are in agreement with the chaotic behaviour of the system.

• Thickness dependence of the structural and electrical properties of ZnO thermal-evaporated thin ﬁlms

ZnO thin ﬁlms of different thicknesses were prepared by thermal evaporation on glass substrates at room temperature. Deposition process was carried out in a vapour pressure of about $5.54 \times 10^{-5}$ mbar. The substrate–target distance was kept constant during the process. By XRD and AFM techniques the microstructural characteristics and their changes with variation in thickness were studied. Electrical resistivity and conductivity of samples vs. temperature were investigated by four-probe method. It was shown that an increase in thickness causes a decrease in activation energy.

• Non-minimal quintessence: Dynamics and coincidence problem

Brans–Dicke scalar–tensor theory provides a conformal coupling of the scalar ﬁeld with gravity in Einstein’s frame. This model is equivalent to an interacting quintessence in which dark matter is coupled to dark energy. This provides a natural mechanism to alleviate the coincidence problem. We investigate the dynamics of this model and show that it leads to comparable dark energy and dark matter densities today.

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Posted on July 25, 2019