By judicious exploitation of the transpose operator relation in conjunction with thedifferential equations of special functions of mathematical physics, integral representations of the on- and off-shell Jost functions are derived from the particular integrals of the inhomogeneous Schrödinger equation. Using the particular integral of the inhomogeneous Schrödinger equation, exact analytical expressions for the Coulomb and Coulomb plus Yamaguchi off-shell Jost solutions are constructed in the maximal reduced form. As a case study, the limiting behaviours and the on-shell discontinuities of the Coulomb plus Yamaguchi Jost solutions are verified numerically.

In the present paper, an analytic solution of nonlinear fractional Fisher equation is deduced with the help of the powerful differential transform method (DTM). To illustrate the method, two examples have been prepared. The method for this equation has led to an exact solution. The reliability, simplicity and cost-effectiveness of the method are confirmed by applying this method on different forms of functional equations.

We investigate both the non-Hermitian parity–time-(PT-)symmetric and Hermitianasymmetric volcano potentials, and present the analytical solution in terms of the confluent Heun function. Under certain special conditions, the confluent Heun function can be terminated as a polynomial, thereby leading to certain exact analytical results. It is found that the non-Hermitian PTsymmetric volcano potentials support the normalizable and non-normalizable reflectionless stateswith real energies. The Hermitian asymmetric volcano potentials allow normalizable reflectionless states with complex energies.

The purpose of this paper is a proposal on entanglement concentration protocol forcluster states. The protocol uses CNOT gate operation and is assisted with a single qubit. Moreover, the local and non-local operations are performed by a single party. We also make a comparative numerical study of the residual entanglement left out after the execution of each step of the protocol.

The quasiexactly solvable potential method is used to determine the energies and the corresponding exact eigenfunctions for a system of N particles with equal mass interacting via an anharmonic potential. For systems with five and seven particles, we compute the ground state and the first excited state only, and compare the spectrums with the results obtained by Ritz approximation method.

We solve the Nakajima–Zwanzig (NZ) non-Markovian master equation to study the dynamics of different types of three-level atomic systems interacting with bosonic Lorentzian reservoirs at zero temperature. Von Neumann entropy (S) is used to show the evolution of the degree of entanglement of the subsystems. The results presented are also compared with some recently published reports.

We present two schemes for transforming bipartite non-maximally entangled states into a W state in cavity QED system, by using highly detuned interactions and the resonant interactions between two-level atoms and a single-mode cavity field. A tri-atom W state can be generated by adjusting the interaction times between atoms and the cavity mode. These schemes demonstrate that two bipartite non-maximally entangled states can be merged into a maximally entangled W state. So the scheme can, in some sense, be regarded as an entanglement concentration process. The experimental feasibility of the schemes is also discussed.

Delay identification from the chaotic intensity output of a quantum dot laser with optical feedback is done using numerical and information theoretic techniques. Four quantifiers, namely autocorrelation function, delayed mutual information, permutation entropy and permutation statistical complexity, are employed in delay estimation. A detailed comparison of these quantifiers with different feedback rates and delay is undertaken. Permutation entropy and permutation statistical complexity are calculated with different dimensions of symbolic reconstruction to obtain the best results.

The development of atmospheric disturbances in the tropical region is explained using vibrational resonance, a nonlinear phenomenon. As the Lorenz system is the most plausible model to describe the convective process in a tropical region, the influence of vertical wind shear and tropical waves on the system leading to tropical cyclone has been investigated. The response of the convective region towards vertical wind shear and tropical waves is numerically studied. It was found that the response of the convective system decreases with the absence of any of these environmental factors. The dynamics of the system including resonance phenomenon is studied using phase portraits and Lyapunov dimension. Further, Lyapunov dimension is employed here to characterize the occurrence of resonant peaks.

Using the auxiliary equation method, we obtain exact solutions of certain nonlinear chemotaxis diffusion reaction equations in the presence of a stimulant. In particular, we account for the nonlinearities arising not only from the density-dependent source terms contributed by the particles and the stimulant but also from the coupling term of the stimulant. In addition to this, the diffusion of the stimulant and the effect of long-range interactions are also accounted for in theconstructed coupled differential equations. The results obtained here could be useful in the studies of several biological systems and processes, e.g., in bacterial infection, chemotherapy, etc.

The band structure of the proton-odd nuclei $^{153,155}$Eu, built on Nilsson orbitals, is investigated within the framework of a recently developed extended Bohr Hamiltonian model. The relative distance between spherical orbitals is taken into account by considering single-particle energies as a parameter which changes with increasing neutron number. Energy levels of each band and$B(E2)$ values inside the ground-state band are calculated and compared with the available experimental data. Thus, more comprehensive information on the structure of deformed nuclei can be obtained by studying the rotation–vibration spectra of odd nuclei built on Nilsson single-particle orbitals.

Limitations of the static Woods–Saxon potential and the applicability of the energy dependent Woods–Saxon potential (EDWSP) model within the framework of one-dimensional Wong formula to explore the sub-barrier fusion data are highlighted. The inelastic surface excitations of the fusing nuclei are found to be dominating in the enhancement of sub-barrier fusion excitation function data and the effects of such dominant vibrational states are exploited through the coupled channel calculations obtained by using the code CCFULL. It is worth mentioning here that the influence of multiphonon vibrational states of the reactants can be simulated by introducing the energy dependence in the nucleus–nucleus potential.

The elastic collision between two ortho-positronium (e.g. $S = 1$) atoms is studied using an {\it ab-initio} static exchange model (SEM) in the centre of mass (CM) frame by considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled channel methodology in momentum space is used to solve Lippman–Schwinger equation following the integral approach. A new SEM code is developed in which the Born–Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. The $s$-, $p$- and $d$-wave elastic phase shifts and the corresponding partial cross-sections for the spin alignment $S = 0$, i.e., singlet (+) and $S = 2$, i.e., triplet (−) states are studied. An augmented Born approximation is used to includethe contribution of higher partial waves more accurately to determine the total/integrated elastic cross-section $(\sigma)$, the quenching cross-section (σq) and ortho-to-para conversion ratio $(\sigma/\sigma q)$. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The theory includes the non-adiabatic short-range effects due to exchange.

Tunable filter based on two metal–insulator–metal (MIM) waveguides coupled to each other by a ring resonator with double narrow gaps is designed and numerically investigated by finitedifference time-domain (FDTD) simulations. The propagating modes of surface plasmon polaritons (SPPs) are studied. By introducing narrow gaps in ring resonators, the transmission in differentresonance modes can be effectively adjusted by changing the gap width (g), and the transmitted peak wavelength has a nonlinear relationship with g. Another structure consisting two cascading ring resonators and regular MIM waveguide have also been proposed. The mechanism based on circular ring resonators with narrow gaps may provide a novel method for designing all-opticalintegrated components in optical communication and computing.

The present paper reports the comparative study of density of defect states (DOS) between bulk samples and thin films of glassy Se$_{90}$Sb$_{10}$. These glasses have been prepared by the quenching technique. Thin films of these glasses have been prepared by vacuum evaporation technique. Space-charge-limited conduction (SCLC) has been measured at different temperatures.The density of localized states near Fermi level is calculated by fitting the data to the theory of SCLC for the case of uniform distribution of localized states for bulk as well as for thin films. A comparison has been made between the density of states calculated in these two cases.

The effect of Ge additive on the physical and dielectric properties of Se$_{75}$Te$_{25}$ and Se$_{85}$Te$_{15}$ glassy alloys has been investigated. It is inferred that on adding Ge, the physical propertiesi.e., average coordination number, average number of constraints and average heat of atomization increase but lone pair electrons, fraction of floppy modes, electronegativity, degree of crosslinking and deviation of stoichiometry (R) decrease. The effect of Ge doping on the dielectric propertiesof the bulk Se$_{75}$Te$_{25}$ and Se$_{85}$Te$_{15}$ glassy alloys has also been studied in the temperature range 300–350 K for different frequencies (1 kHz–5 MHz). It is found that, with doping, the dielectric constant $\epsilon'$ and dielectric loss $\epsilon "$ increase with increase in temperature and decrease with increase in frequency. The role of the third element Ge, as an impurity in the two pure binary Se$_{75}$Te$_{25}$ and Se$_{85}$Te$_{15}$ glassy alloys has been discussed in terms of the nature of covalent bonding and electronegativity difference between the elements used in making the aforesaid glassy systems.

Microstructure of chemically synthesized wurtzite-type CdS nanocrystals have been investigated by X-ray diffraction (XRD) peak profile analysis by applying different forms of Williamson–Hall (WH) method viz., uniform deformation model (UDM), uniform stress deformation model (USDM) and uniform deformation energy density model (UDEDM), and transmission electron microscope (TEM) observations. The WH methods show the average crystallite size to beabout 10 nm. Strain, stress and energy density of the nanocrystals are found to be $1.18 \times 10^{−2}, 0.43$ GPa and $2.27$ kJ m$^{−3}$, respectively. High-resolution TEM (HRTEM) results show the nanocrystals to be in spherical shape with an average crystallite size of 10 nm, thereby complementing the size estimation by WH methods. Further, HRTEM observations reveal the presence of edge dislocations and twin boundaries within the nanocrystals.

Based on the range–energy relationship, the characteristics of secondary electron emission, some relationship between the secondary electron yield $\delta$ and experimental results, the universal formulae for $\delta_{0.8−2}$ (the subscript indicates that the energy range of primary energy atthe surface W$_{\rm po}$ is from 0.8 keV to 2 keV) and $\delta_{2−10}$ for metals were deduced. The $\delta_{0.8−10}$ calculated with the universal formulae and the$\delta_{0.8−10}$ measured experimentally were compared, and the scattering of $\delta$ for the same metal was analysed. Finally, we concluded that the formulae were universal for $\delta_{0.8−10}$ for metals. On the basis of some relationship between parameters of $\delta$, wededuce a formula for expressing total stopping power $S_{0.8−10}$ as a function of $S_{10−30}, \delta_{0.8−10}, \delta_{10−30}$, backscattered coefficient $\heta_{0.8−10}, \heta_{10−30}$ and W$_{\rm po}. The calculated $S_{0.8−10}$ were compared with the values measured experimentally and it was concluded that the formula to estimate $S_{0.8−10}$ was universal for metals.

We investigate the existence and propagation of low-frequency (in comparison to ion cyclotron frequency) electrostatic ion waves in highly dense inhomogeneous astrophysical magnetoplasma comprising relativistic degenerate electrons and non-degenerate ions. The dispersion equation is obtained by Fourier analysis under mean-field quantum hydrodynamics approximationfor various limits of the ratio of rest mass energy to Fermi energy of electrons, relevant to ultrarelativistic, weakly-relativistic and non-relativistic regimes. It is found that the system admits an oscillatory instability under certain condition in the presence of velocity shear parallel to ambient magnetic field. The dispersive role of plasma density and magnetic field is also discussed parametrically in the scenario of dense and degenerate astrophysical plasmas.