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      Volume 70, Issue 3

      March 2008,   pages  381-563

    • Quantum mechanics of rapidly and periodically driven systems

      Malay Bandyopadhyay Sushanta Dattagupta

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      This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a `Kapitza Window' over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.

    • Berry phases in the three-level atoms driven by quantized light fields

      Mai-Lin Liang Zong-Cheng Xu Bing Yuan

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      A theoretical analysis of Berry's phases is given for the three-level atoms interacting with external one-mode and two-mode quantized light fields. Three main results are obtained: (i) There is a Berry phase which vanishes in the classical limit or this Berry phase is completely induced by the field quantization; (ii) Berry's phases for the one-mode field and the two-mode field can be equal so long as the photon numbers of the two-mode field are properly chosen; (iii) In the two-mode case, Berry phases of the atom interacting with one mode is affected by the other mode even if the photon number of the other mode is zero.

    • Remarks on Hawking radiation as tunneling from a uniformly accelerating black hole

      Xiao-Xiong Zeng Jian-Song Hou Shu-Zheng Yang

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      Motivated by the Hamilton-Jacobi method of Angheben et al, we investigate the Hawking tunneling radiation from a uniformly accelerating rectilinear black hole for which the horizons and entropy are functions of 𝜃. After several coordinate transformations, we conclude that when the self-gravitational interaction and energy conservation are taken into account, the actual radiation spectrum deviates from the thermal one and the tunneling rate is the function of 𝜃 though it is still related to the change of the Bekenstein-Hawking entropy.

    • Generalized 𝑁-coupled maps with invariant measure in Bose-Mesner algebra perspective

      M A Jafarizadeh S Behina E Faizi S Ahadpour

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      By choosing a dynamical system with 𝑑 different couplings, one can rearrange a system based on the graph with a given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a relation between the vertexes. Based on the $E_{0}$ transverse projection operator, we addressed synchronization problem of an array of the linearly coupled map lattices of identical discrete time systems. The synchronization rate is determined by the second largest eigenvalue of the transition probability matrix. Algebraic properties of the Bose-Mesner algebra with an associated scheme with definite spectrum has been used in order to study the stability of the coupled map lattice. Associated schemes play a key role and may lead to analytical methods in studying the stability of the dynamical systems. The relation between the coupling parameters and the chaotic region is presented. It is shown that the feasible region is analytically determined by the number of couplings (i.e. by increasing the number of coupled maps, the feasible region is restricted). It is very easy to apply our criteria to the system being studied and they encompass a wide range of coupling schemes including most of the popularly used ones in the literature.

    • The dynamical mixing of light and pseudoscalar ¯elds

      Sudeep Das Pankaj Jain John P Ralston Rajib Saha

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      We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions $L_{\text{int}} = g_{\phi}\phi \epsilon_{\mu \nu \alpha \beta} F^{\mu \nu} F^{\alpha \beta}$. The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.

    • Numerical calculations of potential distribution in non-ideal quadrupole trap and simulations of anharmonic oscillations

      Anita Gupta Pushpa M Rao

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      A quadrupole ion trap consisting of electrode structures symmetric about 𝑧-axis is an important tool for conducting several precision experiments. In practice the field inside the trap does not remain purely quadrupolar, and can be calculated using numerical methods. We have used boundary element method to calculate the potential inside the truncated as well as symmetrically misaligned quadrupolar ion trap. The calculated potential values are fitted to multipole expansion and the weights of multipole moments have been evaluated by minimizing the least square deviation. The higher-order multi-pole contribution in the fabricated hyperbolic electrodes due to truncation and machining imperfections is discussed. Non-linear effects arising due to the superposition of octupole moment manifest as anharmonic oscillations of trapped ions in the non-ideal Paul trap. Theoretical simulations of non-linear effects have been carried out.

    • Determination of experimental K-shell fluorescence yield for potassium and calcium compounds

      E Tiraşoğlu Ö Söğüt

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      K-shell fluorescence yields were experimentally determined for potassium and calcium compounds using a Si(Li) X-ray detector system (FWHM=5.96 keV at 160 eV). The samples were excited by 5.96 keV photons produced by a 55Fe radioisotope source. The experimental values are systematically lower than the theoretical values.

    • Laser Raman and infra-red spectra of biomolecule: 5-aminouracil

      J S Singh

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      Laser Raman (200-4000 cm-1) and IR (200-4000 cm-1) spectra of 5-aminouracil were recorded in the region 200{4000 cm-1. Assuming a planar geometry and C$_{s}$ point group symmetry, it has been possible to assign all the 36 ($25a^{'} + 11a^{''}$) normal modes of vibration for the first time. The two NH bonds of the NH2 group appear to be equivalent as the NH2 stretching frequencies satisfy the empirical relation proposed for the two equivalent NH bonds of the NH2 group. The two NH2 stretching frequencies are distinctly separated from the CH/NH ring stretching frequencies. A strong and sharp IR band at 3360 cm-1 could be identified as the anti-symmetric NH2 mode whereas the band at 3290 cm-1 with smaller density could be identified as the symmetric NH2 stretching mode. All other bands have also been assigned different fundamentals/overtones/combinations.

    • Electron cyclotron resonance breakdown studies in a linear plasma system

      Vipin K Yadav K Sathyanarayana D Bora

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      Electron cyclotron resonance (ECR) plasma breakdown is studied in a small linear cylindrical system with four different gases - hydrogen, helium, argon and nitrogen. Microwave power in the experimental system is delivered by a magnetron at $2.45 \pm 0.02$ GHz in TE10 mode and launched radially to have extra-ordinary (X) wave in plasma. The axial magnetic field required for ECR in the system is such that the fundamental ECR surface ($B = 875.0$ G) resides at the geometrical centre of the plasma system. ECR breakdown parameters such as plasma delay time and plasma decay time from plasma density measurements are carried out at the centre using a Langmuir probe. The operating parameters such as working gas pressure ($1 \times 10^{-5} -1 \times 10^{-2}$ mbar) and input microwave power (160{800 W) are varied and the corresponding effect on the breakdown parameters is studied. The experimental results obtained are presented in this paper.

    • Characteristics of electron cyclotron resonance plasma formed by lower hybrid current drive grill antenna

      P K Sharma S L Rao K Mishra R G Trivedi D Bora

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      A 3.7 GHz system, which is meant for LHCD experiments on ADITYA tokamak, is used for producing ECR discharge. The ECR discharge is produced by setting the appropriate resonance magnetic field of 0.13 T, with hydrogen at a fill pressure of about $5 \times 10^{-5}$ Torr. The RF power, up to 10 kW (of which $\sim 50$% is reflected back), with a typical pulse length of 50 ms, is injected into the vacuum chamber of the ADITYA tokamak by a LHCD grill antenna and is used for plasma formation. The average coupled RF power density (the RF power/a typical volume of the plasma) is estimated to be $\sim 5$ kW/m3. When the ECR appears inside the tokamak chamber for the given pumping frequency ($f = 3.7$ GHz) a plasma with a density ($n_{e}$) $\sim 4 \times 10^{16}$ m-3 and electron temperature $\sim 8$ eV is produced. The density and temperature during the RF pulse are measured by sets of Langmuir probes, located toroidally, on either side of the antenna. $H_{\alpha}$ signals are also monitored to detect ionization. An estimate of density and temperature based on simple theoretical calculation agrees well with our experimental measurements. The plasma produced by the above mechanism is further used to characterize the ECR-assisted low voltage Ohmic start-up discharges. During this part of the experiments, Ohmic plasma is formed using capacitor banks. The plasma loop voltage is gradually decreased, till the discharge ceases to form. The same is repeated in the presence of ECR-formed plasma (RF pre-ionization), formed 10 ms prior to the loop voltage. We have observed that (with LHCD-induced) ECR-assisted Ohmic start-up discharges is reliably and repeatedly obtained with reduced loop voltage requirement and breakdown time decreases substantially. The current ramp-up rates also decrease with reduced loop voltage operation. These studies established that ECR plasma formed with LHCD system exhibits similar characteristics as reported earlier by dedicated ECR systems. This experiment also addresses the issue of whether ECR plasma formed with grill antenna exhibits similar behavior as that formed by single waveguide ECR antenna. Our experimental observations suggest that the characteristics of (LHCD system-induced) ECR-assisted Ohmic start-up discharges show similar properties, reported earlier with normal ECR-assisted Ohmic start-up discharges and hence LHCD system may be used as ECR system at reduced toroidal magnetic field for other applications like wall conditioning.

    • Generation of whistler mode in a relativistic plasma

      N K Deka B J Saikia K S Goswami

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      This paper contains the plasma maser interaction between high frequency nonresonant whistler R-mode and low frequency resonant ion acoustic mode in a relativistic plasma. It shows that the whistler R-mode grows through the plasma maser interaction between the relativistic electrons and the ion acoustic fluctuation.

    • Effects of ion-fluid temperature on dust-ion-acoustic solitons

      Fatema Sayed A A Mamun

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      The properties of dust-ion-acoustic (DIA) solitons in an unmagnetized dusty plasma, whose constituents are adiabatic ion-fluid, Boltzmann electrons, and static dust particles, are investigated by employing the reductive perturbation method. The Korteweg-de Vries equation is derived and its stationary solution is numerically analyzed. The parametric regimes for the existence of positive and negative solitons are found. It has been shown that ion-fluid temperature not only significantly modifies the basic features (width and amplitude) of DIA solitons, but also introduces some new features of DIA solitons.

    • Gd-substituted Bi-2223 superconductor

      D R Mishra

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      The effects of gadolinium doping at calcium site on the normal and super-conducting properties of Bi-2223 system were studied. The Gd-doped (BiPb)-2223 series of specimens, namely Batch I, II and III were sintered at three different sintering temperatures 830, 850 and $895^{\circ}$C respectively. The properties investigated are (1) the normal state resistivity with a view to study metal-to-insulator transition, (2) the XRD patterns of the specimens with a view to study the relative composition of (BiPb)-2212 and (BiPb)-2223 phases and (3) the superconducting fluctuation behaviour (SFB) with a view to determine the effect of doping, if any, on the dimensionality of the fluctuation conductivity of the system. The normal state resistivity of Gd-substituted Bi-2223 specimens shows metallic, semiconducting and insulating behaviour. The $T_{c}(R = 0)$ values indicate that (BiPb)-2223 phase is responsible for the observed superconducting transitions in Batch I and Batch II specimens with Gd concentrations $x \leq 0.7$. This observation is further confirmed in the analysis of XRD patterns of these specimens. Gadolinium, being a magnetic impurity, has pair breaking effect near the Fermi level and decreases $T_{c}(R = 0)$. The analysis of the superconducting fluctuation behaviour (SFB) shows a 2D dimensionality without any cross-over.

    • Dielectric relaxation of binary polar liquid mixture measured in benzene at 10 GHz frequency

      S Sahoo K Dutta S Acharyya S K Sit

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      The dielectric relaxation times $\tau_{jk}$'s and dipole moments $\mu_{jk}$'s of the binary ($j_{k}$) polar liquid mixture of N,N-dimethyl acetamide (DMA) and acetone (Ac) dissolved in benzene (i) are estimated from the measured real $\sigma_{ijk}^{'}$ and imaginary $\sigma_{ijk}^{''}$ parts of complex high frequency conductivity $\sigma_{ijk}^{*}$ of the solution for different weight fractions $w_{jk}$'s of 0.0, 0.3, 0.5, 0.7 and 1.0 mole fractions $x_{j}$ of Ac and temperatures (25, 30, 35 and 40°C) respectively under 9.88 GHz electric field. $\tau_{jk}$'s are obtained from the ratio of slopes of $\sigma_{ijk}^{''} - w_{jk}$ and $\sigma_{ijk}^{'} - w_{jk}$ curves at $w_{jk} \rightarrow 0$ as well as linear slope of $\sigma_{ijk}^{''} - \sigma_{ijk}^{'}$ curves of the existing method (Murthy et al, 1989) in order to eliminate polar-polar interaction in the latter case. The calculated 𝜏's are in excellent agreement with the reported 𝜏's due to Gopalakrishna's method. $\mu_{jk}$'s are also estimated from slopes 𝛽's of total conductivity $\sigma_{ijk} - w_{jk}$ curves at $w_{jk} \rightarrow 0$ and the values agree well with the reported 𝜇's from G.K. method. The variation of $\tau_{jk}$'s and $\mu_{jk}$'s with $x_{j}$ of Ac reveals that solute-solute molecular association occurs within $0.0-0.3x_{j}$ of Ac beyond which solute-solvent molecular association is predicted. The theoretical dipole moments $\mu_{\text{theo}}$'s are calculated from bond angles and bond moments to have exact 𝜇's only to show the presence of inductive, mesomeric and electromeric effects in the substituent polar groups. The thermodynamic energy parameters are estimated from ln($\tau_{jk}T$) against $1/T$ linear curve from Eyring's rate theory to know the molecular dynamics of the system and to establish the fact that the mixture obeys the Debye-Smyth relaxation mechanism.

    • Laser-induced breakdown spectroscopy: A versatile tool for monitoring traces in materials

      Shiwani Pandhija A K Rai

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      Laser-induced breakdown spectroscopy (LIBS) is an emerging technique for simultaneous multi-elemental analysis of solids, liquids and gases with minute or no sample preparation and thus revolutionized the area of on-line analysis technologies. The foundation for LIBS is a solid state, short-pulsed laser that is focused on a sample to generate a high-temperature plasma, and the emitted radiation from the excited atomic and ionic fragments produced within the plasma is characteristic of the elemental composition of the sample that can be detected and analyzed using a suitable optical spectrograph. In the present paper, the applicability of LIBS for different solid samples having homogeneous (silver ornament, aluminum plate) or heterogeneous composition (soil) using nanosecond laser pulses is discussed. Nanosecond pulse laser makes plasma at the sample surface even at very low pulse energies and also allows for precise ablation of the substrate material with little damage to the surrounding area. We have also studied the penetration of different heavy metals inside the soil surface.

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