Volume 67, Issue 6
December 2006, pages 999-1192
pp 999-1009 December 2006 Research Articles
Construction of exact complex dynamical invariant of a two-dimensional classical system
We present the construction of exact complex dynamical invariant of a two-dimensional classical dynamical system on an extended complex space utilizing Lie algebraic approach. These invariants are expected to play a vital role in understanding the complex trajectories of both classical and quantum systems.
pp 1011-1022 December 2006 Research Articles
Exact solutions to a class of nonlinear Schrödinger-type equations
Jin-Liang Zhang Ming-Liang Wang
A class of nonlinear Schrödinger-type equations, including the Rangwala-Rao equation, the Gerdjikov-Ivanov equation, the Chen-Lee-Lin equation and the Ablowitz-Ramani-Segur equation are investigated, and the exact solutions are derived with the aid of the homogeneous balance principle, and a set of subsidiary higher order ordinary differential equations (sub-ODEs for short).
pp 1023-1035 December 2006 Research Articles
Spectral inverse problem for q-deformed harmonic oscillator
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent q-deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of q-deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this spectral inverse method.
pp 1037-1041 December 2006 Research Articles
Cosmic no-hair conjecture in scalar-tensor theories
We have shown that, within the context of scalar-tensor theories, the anisotropic Bianchi-type cosmological models evolve towards de Sitter Universe. A similar result holds in the case of cosmology in Lyra manifold. Thus the analogue of cosmic no-hair theorem of Wald [1] hold in both the cases. In fact, during inflation there is no difference between scalar-tensor theories, Lyra’s manifold and general relativity (GR).
pp 1043-1053 December 2006 Research Articles
Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations
U Camci Z Can Y Nutku Y Sucu D Yazici
We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang’s J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac’s theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints are second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac’s theory. Finally, we present the Bäcklund transformation between the J- and K-gauges in order to apply Magri’s theorem to the respective two Hamiltonian structures.
pp 1055-1071 December 2006 Research Articles
The quantum dynamics of an electron moving under the Henon-Heiles (HH) potential in the presence of external time-dependent (TD) laser fields of varying intensities have been studied by evolving in real time the unperturbed ground-state wave function φ (x, y, t) of the HH oscillator. The TD Schrödinger equation is solved numerically and the system is allowed to generate its own wave packet. Two kinds of sensitivities, namely, sensitivity to the initial quantum state and to the Hamiltonian, are examined. The threshold intensity of the laser field for an electron moving in the HH potential to reach its continuum is identified and in this region quantum chaos has been diagnosed through a combination of various dynamical signatures such as the autocorrelation function, quantum ‘phase-space’ volume, ‘phase-space’ trajectory, distance function and overlap integral (akin to quantum fidelity or Loschmidt echo), in terms of the sensitivity towards an initial state characterized by a mixture of quantum states (wave packet) brought about by small changes in the Hamiltonian, rather than a ‘pure’ quantum state (a single eigenstate). The similarity between the HH potential and atoms/molecules in intense laser fields is also analyzed.
pp 1073-1086 December 2006 Research Articles
Hierarchy of rational order families of chaotic maps with an invariant measure
M A Jafarizadeh M Foroutan S Ahadpour
We introduce an interesting hierarchy of rational order chaotic maps that possess an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps [1–5], with merely entropy production, the rational order chaotic maps can simultaneously produce and consume entropy. We compute the Kolmogorov-Sinai entropy of these maps analytically and also their Lyapunov exponent numerically, where the obtained numerical results support the analytical calculations.
pp 1087-1097 December 2006 Research Articles
Soumen Bhattacharyya Anita Gupta SG Nakhate Pushpa M Rao
Europium (Eu^{+}) ions were confined in a Paul trap and detected by non-destructive method. Storage time of Eu^{+} ions achieved in vacuum was improved by orders of magnitude employing buffer gas cooling. The experimentally detected signal was fitted to the ion response signal and the total number of ions trapped was estimated. It is found that the peak signal amplitude as well as the product of FWHM and the peak signal amplitude is proportional to the total number of trapped ions. The trapped ion secular frequency was swept at different rates and its effect on the absorption line profile was studied both experimentally and theoretically.
pp 1099-1118 December 2006 Research Articles
Sulagna Dutta Krishna Rai Dastidar
Dependence of amplification without inversion (AWI) on the relative strength of probe and coherent field Rabi frequencies has been studied in H_{2} and LiH molecules for three-level Λ configuration. We have derived exact analytical expressions for coherences and populations keeping all the orders of probe field Rabi frequency (G) and coherent field Rabi frequency. (Θ) in the steady state limit. Previously, first-order approximation (i.e. keeping only the first-order term in G) was used and hence AWI was studied for the condition Θ>>G. Here, by using the exact analytical expressions of coherences and populations, we have shown that AWI is maximum when Θ is within the same order of probe field Rabi frequency G irrespective of the choice of different ro-vibrational transitions in both the molecules. However, the shape of the gain profile and the maximum value of gain on the probe field and the absorption on coherent field depend on the choice of different ro-vibrational levels as the upper lasing levels. Effect of bidirectional pumping, homogeneous and inhomogeneous broadening on AWI process has been studied. By solving the density matrix equations numerically it has been shown that both the transient and the steady state AWI can be obtained and the numerical values of coherences and populations at large time are in very good agreement with exact analytical values in the steady state limit. It has been shown that in molecules AWI can be obtained on probe field of smaller wavelength than that of the coherent field which has not been observed in atoms so far.
pp 1119-1128 December 2006 Research Articles
Pulsed pump: Thermal effects in solid state lasers under super-Gaussian pulses
Solid state laser (SSL) powers can be realistically scaled when pumped by a real, efficient and multimode pulse. In this work, a fourth-order super-Gaussian pulse was assumed as a pump for SSL’s and a complete analytical expression for the thermal phase shift is given. Moreover, the focal length of thermal lens in paraxial ray approximation regime was studied. The results when applied to a Ti: sapphire crystal show an appreciable correction for abberation compared to a top-hat pulse.
pp 1129-1140 December 2006 Research Articles
Mode-to-mode energy transfers in convective patterns
Mahendra K Verma Krishna Kumar Bhask Ar Kamble
We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R_{c}. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.
pp 1141-1154 December 2006 Research Articles
We have carried out Monte Carlo simulations in Gibbs ensemble for two-and three-dimensional double Yukawa fluid. We have compared liquid-vapour equilibrium curve with that of Lennard-Jones, when parameters occurring in double Yukawa potential are chosen to fit Lennard-Jones potential. The results are in good agreement. The role of repulsive and attractive contributions for the potential on the liquid-vapour coexistence region as well as on critical temperature and critical density has been studied. The critical temperature is found to be more sensitive than the critical density to the variation in repulsive and attractive parts of the potential. Also, the range of the attractive interaction directly influences range of the liquid vapour coexistence region. It has been found that smaller the values of the attractive parameter, larger is the coexistence region.
pp 1155-1164 December 2006 Research Articles
Photonic band gap engineering in 2D photonic crystals
The polarization-dependent photonic band gaps (TM and TE polarizations) in two-dimensional photonic crystals with square lattices composed of air holes in dielectric and vice versa i.e., dielectric rods in air, using the plane-wave expansion method are investigated. We then study, how the photonic band gap size is affected by the changing ellipticity of the constituent air holes/dielectric rods. It is observed that the size of the photonic band gap changes with changing ellipticity of the constituent air holes/dielectric rods. Further, it is reported, how the photonic band gap size is affected by the change in the orientation of the constituent elliptical air holes/dielectric rods in 2D photonic crystals.
pp 1165-1171 December 2006 Research Articles
Modelling of the magnetic and magnetostrictive properties of high permeability Mn-Zn ferrites
This paper presents the results of modelling of both magnetic and magnetostrictive properties of high permeability Mn_{0.51}Zn_{0.44}Fe_{2.05}O_{4} ferrites. The parameters of energy-based Jiles-Atherton-Sablik (J-A-S) model were calculated for each experimental hysteresis loop on the basis of evolutionary strategies and Hook-Jevis optimization method. Finally, high conformity between experimental and modelling results was achieved. This high conformity indicates that the presented results create new opportunity of modelling of the properties of inductive components based on ferrites as well as quantitative description of magnetization process.
pp 1173-1178 December 2006
pp 1179-1185 December 2006
pp 1186-1192 December 2006
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