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      Volume 93, Issue 5

      November 2019

    • Violation of space–time Bell-CHSH inequality beyond the Tsirelson bound and quantum cryptography

      C S SUDHEER KUMAR

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      Here we show that if we insert context-dependent local unitary evolutions into the spatial (i.e. normal) Bell–Clauser–Horne–Shimony–Holt (Bell-CHSH) test, then it is possible to violate the space–time Bell-CHSH inequality maximally (i.e. up to 4). The correct context dependency can be achieved via post-selection. However, this does not contradict the Tsirelson quantum bound ($2\sqrt{2}$), because the latter has been derived without taking into consideration the context-dependent unitary evolutions and/or post-selection. As an important application, this leads to a more efficient (in terms of resource (singlets) and classical communication) and more sensitive (to eavesdropping) quantum key distribution (QKD) protocol, compared to Ekert’s and Wigner’s QKD protocols.

    • $q$-Deformed oscillator algebra in fermionic and bosonic limits

      S SARGOLZAEIPOR H HASSANABADI W S CHUNG A N IKOT

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      In this paper, the structure function corresponding to the $q$-deformed harmonic oscillator algebra is considered, where we construct the Hamiltonian by using creation and annihilation operators. Finally, the problem is investigated by evaluating the partition function of the system in finite- and infinite-dimensional Fock space for both fermionic and bosonic limits. Other thermodynamic properties such as the internal energy and the specific heat of the system are also calculated.

    • Robustness of coherence for multipartite quantum states

      CHIRANJIB MUKHOPADHYAY UDIT KAMAL SHARMA INDRANIL CHAKRABARTY

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      In this brief report, we prove that the robustness of coherence (ROC), in contrast with many popular quantitative measures of quantum coherence derived from the resource-theoretic framework of coherence, may be a subadditive for a specific class of multipartite quantum states. We investigate how the subadditivity is affected by admixture with other classes of states for which ROC is superadditive. We show that pairs of quantum states may have different orderings with respect to relative entropy of coherence, $l_{1}$-norm of coherence and ROC and numerically study the difference in ordering for the chosen pairwise coherence measures.

    • A chaotic study on Heisenberg ferromagnetic spin chain using Dzyaloshinski–Moriya interactions

      B S GNANA BLESSY M M LATHA

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      The chaotic dynamics of a one-dimensional Heisenberg ferromagnetic spin chain incorporating Dzyaloshinski–Moriya (D–M) interaction, dipole–dipole and quadrupole–quadrupole interactions has been investigated. The studies are carried out by plotting phase diagrams and chaotic trajectories. We then analyse the stability of the system using the Lyapunov stability analysis.

    • Solitary waves in strongly non-local media with a harmonic potential

      YUN-ZHOU SUN QIN WU MIN WANG JING-YAN LI

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      An exact analytical solution in strongly non-local media with a harmonic potential has been studied. Two-dimensional Bessel solitary wave clusters have been obtained by a self-similar method. The intensity distributions of optical beam with different parameters have been discussed in detail. It is found that the solitary waves have a symmetric necklace distribution and the number of facular points is double the value of the quantum number $m$. The modulation of the external potential field to the width of light beam is also discussed.

    • Analysis with relativistic mean-field density distribution of elastic scattering cross-sections of carbon isotopes ($^{10–14,16}\rm{C}$) by various target nuclei

      M AYGUN

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      A microscopic study of elastic scattering of carbon isotopes from different target nuclei at various incident energies is presented by using density distributions derived for $^{10–14,16}\rm{C}$ nuclei using relativistic mean field (RMF) theory. To obtain the real part of the optical potential, the double folding model is used.Woods–Saxon potential is used for the imaginary part. The theoretical results are discussed and compared with each other as well as with the experimental data. It is seen that the agreement between theoretical results and experimental data is very good. Also, new global equations for the imaginary potentials of the $^{10–14,16}\rm{C}$ nuclei are derived from the results of the theoretical analysis.

    • Modelling and characterisation of the noise characteristics of the vertical cavity surface-emitting lasers subject to slow light feedback

      HAMEEDA R IBRAHIM MOHAMED S ALGHAMDI AHMED BAKRY MOUSTAFA AHMED FUMIO KOYAMA

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      This paper introduces the modelling and characterisation of the noise properties of the vertical cavity surface-emitting laser (VCSEL) coupled in lateral direction with a passive cavity. This design of VCSEL with this transverse coupled cavity (TCC) is proposed for high-speed photonics. We introduce comprehensive simulationson the influence of the induced lateral slow light feedback on the relative intensity noise (RIN) and carrier-to-noise ratio (CNR). The proposed model incorporates multiple round trips of slow light in the TCC as time delay light in the rate equations of the VCSEL. The obtained results are compared with those of the conventional VCSEL.We show that the noise performance of the TCC-VCSEL is optimised when the VCSEL exhibits stable continuous wave (CW) operation under strong slow light feedback and the TCC length is smaller than 8 $\mu$m and between 11 and 13 $\mu$m. When strong slow light induces unstable regular and/or irregular oscillations, RIN is enhanced and CNR is lowered.

    • Successive linearisation approach to analyse thermally radiative stagnation point micropolar nanofluid flow with regression model

      B KUMAR G S SETH R NANDKEOLYAR

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      The present paper is devoted to the investigation of magnetohydrodynamics (MHD) mixed convection stagnation point flow of a micropolar nanofluid with thermal radiation, microrotation, viscous and Joule dissipations, Brownian and thermophoretic diffusions, etc. The present analysis is done because it contains large potential to deal with many industrial processes such as electrical power generation, nuclear energy plant, melt spinning technique for cooling liquids, astrophysical flows, space vehicles, geothermal extractions, solar system, etc. The numerical solutions of the governing equations are obtained by successive linearisation method (SLM). The influence of various developing parameters, such as thermal radiation parameter, mixed convection parameter, thermophoretic parameter, etc., on the flow field is examined through graphs by accumulating sufficient data using SLM. A comparative study is performed between our results and previously obtained results in the limiting sense. Apart from this, the quadratic multiple regression analysis is performed for skin friction coefficient. It indicates that when the free stream is moving with less velocity than stretching velocity then a small variation in microrotation leads to large perturbation in skin friction in comparison to mixed convection parameter but in the opposite case, the buoyancy force becomes more dominant.

    • An efficient technique for a fractional-order system of equations describing the unsteady flow of a polytropic gas

      P VEERESHA D G PRAKASHA HACI MEHMET BASKONUS

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      In the present investigation, the $q$-homotopy analysis transform method ($q$-HATM) is applied to find approximated analytical solution for the system of fractional differential equations describing the unsteady flow of a polytropic gas. Numerical simulation has been conducted to prove that the proposed technique is reliable and accurate, and the outcomes are revealed using plots and tables. The comparison between the obtained solutions andthe exact solutions shows that the proposed method is efficient and effective in solving nonlinear complex problems. Moreover, the proposed algorithm controls and manipulates the obtained series solution in a huge acceptable region in an extreme manner and it provides us a simple procedure to control and adjust the convergence region of the series solution.

    • Higher-dimensional fractional time-independent Schrödinger equation via fractional derivative with generalised pseudoharmonic potential

      TAPAS DAS UTTAM GHOSH SUSMITA SARKAR SHANTANU DAS

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      In this paper, we obtain approximate bound-state solutions of $N$-dimensional time-independent fractional Schrödinger equation for the generalised pseudoharmonic potential which has the form $V(r^{\alpha}) = a_{1}r^{2\alpha} + (a_{2}/r^{2\alpha}) + a_{3}$. Here $\alpha$ (0 < $\alpha$ < 1) acts like a fractional parameter for the space variable $r$. The entire study consists of the Jumarie-type fractional derivative and the elegance of Laplace transform. As a result, we can successfully express the approximate bound-state solution in terms of Mittag–Leffler function and fractionally defined confluent hypergeometric function. Our study may be treated as a generalisation of all previous workscarried out on this topic when $\alpha = 1$ and $N$ arbitrary. We provide numerical result of energy eigenvalues and eigenfunctions for a typical diatomic molecule for different α close to unity. Finally, we try to correlate our work with a Cornell potential model which corresponds to $\alpha = 1/2$ with $a_{3} = 0$ and predicts the approximate mass spectra of quarkonia.

    • The energy fluxes of surface waves propagating along the interface between nonlinear media with different characteristics

      S E SAVOTCHENKO

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      We describe analytically the nonlinear surface waves at the interface between two nonlinear media with different characteristics. We use one-dimensional nonlinear Schrödinger equation with cubic nonlinearity differing on the opposite sides of the interface. We take into account the interaction of excitations with media interface. We consider the interaction of the wave with the interface using the local potential approximated by Dirac delta function. We derive and analyse three types of dispersion equations determining the surface wave frequencies. We propose two approaches to determine the flux depending on the choice of one of the possible control parameters. We calculate the energy flux of the surface waves and analyse the influence of intensity interaction of excitations with interface and difference of media characteristics on the opposite sides of the interface.

    • Tsallis holographic dark energy in Bianchi-I Universe using hybrid expansion law with $k$-essence

      VIPIN CHANDRA DUBEY SHIKHA SRIVASTAVA UMESH KUMAR SHARMA ANIRUDH PRADHAN

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      In this paper, the proposed dark energy, Tsallis holographic dark energy (THDE), infrared cut-off with the Hubble horizon has been investigated in the Bianchi-I (axially symmetric) anisotropic model with a hybrid expansion law. It has been observed that the THDE is in tune with the accelerating Universe with equation of state (EoS) parameter ($\omega_{T}$ < $−1/3$) in the $k$-essence region. We have used the statefinder diagnostic in our model. In addition, we try to accommodate the perspective of dark energy by the avenue of reconstructing the evolution of scalar field potential. We have considered the $k$-essence for the analysis of this reconstruction, showing the accelerated expansion at present.

    • A unified theory of gravity and electromagnetism: Classical and quantum aspects

      PARTHA GHOSE

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      A unified classical theory of gravity and electromagnetism with a torsion vector $\Gamma_{i} \neq 0$, proposed by S N Bose in 1952, is introduced. In this theory, the torsion vector acts as a magnetic current and it is shown that (i) the electromagnetism is invariant under continuous Heaviside–Larmor transformations and (ii) the electric and magnetic charges are topologically quantised, satisfying the Dirac quantisation condition, without implying any Dirac string provided $\Gamma_{i}$ is curl-less.

    • Stability and chaotic dynamics of forced $\phi^{8}$ generalised Liénard systems

      CLÉMENT HODÉVÈWAN MIWADINOU ADJIMON VINCENT MONWANOU LAURENT AMOUSSOU HINVI JEAN BIO CHABI OROU

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      This work studies a forced generalised Liénard oscillator with $\phi^{8}$ potential with order 8 dissipation. The fixed points and their stability have been analysed for autonomous and non-dissipative Liénard oscillator. The system can exhibit three, five or seven fixed points and the corresponding stability diagram is checked and analysed. The effect of restoring parameters on the potential is also studied. Periodic, multiperiodic and chaotic monostable and bistable attractors and their coexistence have been checked through the bifurcation diagram, Lyapunov exponent, phase space and Poincaré section using the fourth-order Runge–Kutta algorithm. The results obtained by the analytical methods are validated and complemented by the numerical simulations.

    • Systematic study of the $\alpha$ decay properties of actinides

      G R SRIDHARA H C MANJUNATHA K N SRIDHAR H B RAMALINGAM

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      This work analyses the $\alpha$ decay properties of actinides. Geiger–Nuttall plots are presented for actinides. We have studied the competition between $\alpha$ decay and spontaneous fission and have identified the dominant decay mode. The results have been compared with experiments and they agree well with those of the experiments.

    • A novelty to the nonlinear rotating Rayleigh–Taylor instability

      YUSRY O EL-DIB GALAL M MOATIMID AMAL A MADY

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      This paper presents a novel approach for studying the nonlinear Rayleigh–Taylor instability (RTI). The system deals with two rotating superposed infinite hydromagnetic Darcian flows through porous media under the influence of a uniform tangential magnetic field. The field allows the presence of currents on the surface of separation. The appropriate linear governing equations are solved and confirmed with the corresponding nonlinear boundary conditions. A nonlinear characteristic of the surface deflection is deducted. Away from the traditional techniques of the stability analysis, the work introduces a new one. The analysis depends mainly on the homotopy perturbation method (HPM). To achieve an analytical approximate periodic solution of the surface deflection, the secular terms are removed. This cancellation resulted in well-known amplitude equations. These equations are utilised to achieve stability criteria of the system. Therefore, the stability configuration is exercised in linear aswell as nonlinear approaches. The mathematical procedure adopted here is simple, promising and powerful. The method may be used to treat more complicated nonlinear differential equations that arise in science, physics andengineering applications. A numerical calculation is performed to graph the implication of various parameters on the stability picture. In addition, for more convenience, the surface deflection is depicted.

    • Ultrasonic wave propagation in thermoelectric $\rm{ZrX_{2} (X = S, Se)}$ compounds

      SHAKTI PRATAP SINGH GAURAV SINGH ALOK KUMAR VERMA P K YADAWA R R YADAV

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      In the present work,we have calculated temperature-dependent second- and third-order elastic constants (SOECs and TOECs) of thermoelectric zirconium disulphide $\rm{(ZrS_{2})}$ and zirconium diselenide $\rm{(ZrSe_{2})}$ using a simple interaction potential model. SOECs have been used for the calculation of ultrasonic velocity along different orientations of propagation. Thermal relaxation time and ultrasonic attenuation have been determined with the help of SOECs and thermal conductivity. Temperature-dependent specific heat, thermal energy density, elastic coupling constants and Grüneisen parameters are also calculated using SOECs and other parameters. The dominating cause behind ultrasonic attenuation, in the temperature range of 300–900 K, is the interaction of acoustical phonon and lattice phonon. In the present study, we observed that the thermal conductivity and energy density play significant roles in ultrasonic attenuation. Ultrasonic velocity and attenuation are correlated with other thermophysical properties extracting important information about the quality and nature of the materials which are useful for industrial applications.

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