Table of contents

In this paper, based on a system of the first order differential equations with three nonlinear ordinary differential equations (ODEs), a new tri-function method is presented to investigate exact solutions of a wide class of nonlinear wave equations. The method is constructive and can be carried out in a computer with the aid of symbolic computation. In particular, we apply the tri-function method to the (3+1)-dimensional Kadomtsev–Petviashvili (KP) equation and the (2+1)-dimensional nonlinear Schrödinger (NLS) equation such that many types of new exact solutions are obtained, which contain doubly periodic solutions and solitary wave solutions.

For the unitary evolution of the ideal three-mode parametric oscillator, we derive an autonomous system of first order nonlinear differential equations. We show that this autonomous system passes the Painlevé test. Then we show that the system is integrable in the sense of Liouville.

Based on the Einstein–Podolsky–Rosen (EPR) entangled state representation, we show that the complex Wigner transform for the complex function ψ(η) turns out to be the quantum statistical average of the entangled Wigner operator in the state |ψ⟩. The complex fractional Fourier transform is also introduced, which corresponds to a rotation of the complex Wigner function. Thus, the intrinsic relation between the complex Wigner transform and the EPR entangled state is revealed.

Meaningful and well-founded physical quantities are convincingly determined by eigenvalue problem solutions emerging from a second-order N-coupled system of differential equations, known as the Sturm–Liouville matrix boundary problem. Via the generalized Schur decomposition procedure and imposing to the multicomponent system to be decoupled, which is a widely accepted remarkable physical situation, we have unambiguously demonstrated a simultaneously triangularizable scenario for (2N×2N) matrices content in a generalized eigenvalue equation.

On the basis of the modified four-coherent-state post-selection quantum key distribution protocol (Namiki and Hirano 2006 Preprint quant-ph/0608144v1), two 1-out-of-2 quantum oblivious transfer (QOT₂¹) protocols are proposed. The first proposed protocol (called the receiver-based QOT₂¹ protocol) requires the coherent states to be prepared by the receiver, whereas the second protocol (called the sender-based QOT₂¹ protocol) allows the coherent states to be generated by the sender. The main advantages of the proposed protocols are that (i) no quantum bit commitment schemes and the assumption of quantum memory are needed; (ii) less communication cost between participants is required, i.e. the receiver-based QOT₂¹ protocol requires only one quantum communication and one classical communication and the sender-based QOT₂¹ protocol requires only one quantum communication between participants during protocol execution; and (iii) the utilization of quantum states is very efficient, wherein the receiver-based and the sender-based QOT₂¹ protocols use only two coherent pulses and one coherent pulse respectively for sending the sender's two messages.

We study the influence of a generalized uncertainty principle (GUP) on the energy spectrum of (1+1)-dimensional Dirac equation with a linear scalar-like confining potential. We find the dominant contribution to the relativistic energy levels in linear potential field from the deformation of the Dirac equation through the generalized Heisenberg algebra of a GUP. Obviously, our study ends with an approximation, but it sheds much light on a very interesting theoretical physics problem that is not only of theoretical value, but also of natural value.

We discuss the Bohmian paths of two-level atoms moving in a waveguide through an external resonance-producing field, perpendicular to the waveguide and localized in a region of finite diameter. The time spent by a particle in a potential region is not well-defined in standard quantum mechanics, but it is well defined in Bohmian mechanics. Bohm's theory is used for calculating the average time spent by a transmitted particle inside the field region and the arrival-time distributions at the edges of the field region. Using the Runge–Kutta method for the integration of the guidance law, some Bohmian trajectories were also calculated. Numerical results are presented for the special case of a Gaussian wave packet.

The spectrum of the attractive delta-shell potential is investigated in the D-dimensional space (D⩾2). A compact expression for the eigenvalues is derived in the large coupling constant limit for odd dimensions D. With respect to the ground state energy, the spectrum is rotational, being proportional to L(L+D-2), where L is the grand orbital momentum. Extension to even D is achieved on the grounds of the Hellmann–Feynman theorem. Simulating a delta-shell potential by a normalized Gaussian, we discuss finite range effects.

In this paper, we show how to construct a general class of non-relativistic quantum systems with position-dependent masses, which are isospectral to a given system with constant mass. Then, we use this approach in order to construct the Wigner functions in three examples which are isospectral to the harmonic oscillator. Finally, we discuss possible general behavior of these systems.

A few white dwarfs, located in binary systems, may acquire sufficiently high mass-accretion rates resulting in the burning of carbon and oxygen under nondegenerate conditions forming an O+Ne+Mg core. These O+Ne+Mg cores are gravitationally less bound than more massive progenitor stars and can release more energy due to the nuclear burning. They are also amongst the probable candidates for low entropy r-process sites. Recent observations of subluminous Type II-P supernovae (e.g. 2005cs, 2003gd, 1999br and 1997D) were able to rekindle the interest in 8–10 M_⊙ which develop O+Ne+Mg cores. Microscopic calculations of capture rates on ²⁴Mg, which may contribute significantly to the collapse of O+Ne+Mg cores, using the shell model and the proton–neutron quasiparticle random-phase approximation (pn-QRPA) theory, were performed earlier and comparisons made. Simulators, however, may require these capture rates on a fine scale. For the first time, a detailed microscopic calculation of the electron and positron capture rates on ²⁴Mg on an extensive temperature–density scale is presented here. This type of scale is more appropriate for interpolation purposes and of greater utility for simulation codes. The calculations are done using the pn-QRPA theory using a separable interaction. The deformation parameter, believed to be a key parameter in QRPA calculations, is adopted from experimental data to increase the reliability of the QRPA results further. The resulting calculated rates are up to a factor of 14 or more enhanced as compared to shell model rates and may lead to some interesting scenarios for core collapse simulators.

Generalized coherent states associated with SU(1,1) Lie algebra are reviewed. A state is called intelligent if it satisfies the strict equality in the Heisenberg uncertainty relation. The eigenvalue problem satisfied by intelligent states (IS) is solved. The IS associated with SU(1,1) Lie algebra are investigated. We have constructed some realizations for our results of IS, and some applications are discussed. Some nonclassical properties such as Glauber second-order correlation function, photon number distribution and squeezing are investigated.

The propagation of shock waves in a dusty gas with heat conduction and radiation heat flux, in which density varies exponentially, is investigated. The dusty gas is assumed to be a mixture of small solid particles and a perfect gas. The equilibrium flow conditions are assumed to be maintained, and the heat conduction is expressed in terms of Fourier's law and the radiation is considered to be of the diffusion type for an optically thick grey gas model. The thermal conductivity K and the absorption coefficient α_R are assumed to vary with temperature and density. The shock wave moves with variable velocity and the total energy of the wave is non-constant. Non-similar solutions are obtained and the effects of variation of the heat transfer parameters and time are investigated. The effects of an increase in (i) the mass concentration of solid particles in the mixture and (ii) the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are also investigated at given times.

The achievement of the first plasma has demonstrated that the Experimental Advanced Superconducting Tokamak (EAST) engineering construction is completely successful. Divertor plasma discharge with double null configuration was achieved and verified by the fitting codes. Arrays of 60 tilted divertor probes have been installed in the lower, both inboard and outboard, divertor plates of EAST. Evolution of electron temperature and density is obtained by using triple-probe systems; real-time particle flux and power flux at divertor target plates have been measured. Tilted Langmuir triple probes (TLTPS) have been successfully used for measuring edge plasma parameters. The strike point by the fitting codes coincides well with measured edge plasma parameters.

The quantum oscillatory screening effects on the charge capture process are investigated in quantum plasmas. The Bohr–Lindhard formalism with the modified Debye–Hückel potential is employed for obtaining the electron capture radius and probability as functions of the quantum wave number, projectile energy and ion charge number. It is shown that the oscillatory screening effects suppress the electron capture cross section as well as the capture radius. It is also shown that the electron capture radius increases with decreasing quantum wave number. The oscillatory screening effects on the capture radius are found to increase with an increase of the quantum wave number and the ion charge number. In addition, the domain of the capture cross section is found to decrease due to the quantum oscillatory screening effects and also reduces with an increase of the quantum wave number.

The lower hybrid drift instability (LHDI) in a Harris current sheet with negative ions is investigated using the kinetic theory. Numerical results show that the negative ions have considerable effect on the LHDI. With increase of the negative-ion concentration, the growth rate of the LHDI increases and its real frequency decreases for any wave length. The Harris current sheet can thus be significantly modified.

Epitaxial LaNiO₃ (001) thin films with an SrTiO₃/TiN template layer have been deposited on Si(001) single crystal substrates by rf sputtering. The epitaxial growth of LaNiO₃ was achieved in an Ar/O₂ environment at low substrate temperatures from 140 to 310 °C. The orientation relationship was determined to be LaNiO₃(001)[110]∥SrTiO₃(001)[110]∥TiN(001)[110]∥Si(001)[110]. The deposited LaNiO₃ films show a smooth and featureless surface with roughness below 1 nm. These smooth and crack-free LaNiO₃ films provide promising electrodes for the subsequent epitaxial growth of ferroelectric thin films.

The escape rate in the gene transcriptional regulatory system with time delay in the presence of cross-correlation noises is studied. The expression of the escape rate is derived under the condition of small delay time. Based on the escape rate, we investigated the effects of both cross-correlation intensity (λ) and delay time (τ) on the escape rate. Our results indicate that: (i) under positively correlated noises action (i.e. λ> 0), the escape rate exhibits one minimum value as the intensities of the multiplicative and additive noises vary, namely the suppression effect. However, for the case of uncorrelated noises (λ=0) and negatively correlated noises (λ<0), the suppression phenomenon disappears. (ii) λ and τ have opposite effects on the escape rate of the system, i.e. under positively correlated noises action, an increase of λ can intensify the suppression of the escape rate, but an increase of τ can weaken the suppression of the escape rate.

Two-dimensional crystallization of charged paramagnetic colloidal particles by adjusting the coupling parameter was investigated using digital video microscopy. A phase transition from a dispersed distribution to a highly ordered colloidal crystal was achieved when we adjusted the electro and magnetostatic interparticle interactions. The crystallization process of the colloidal monolayer was characterized quantitatively in terms of the radial pair distribution function. The subtle competition between the repulsive interparticle potential energy and thermal excitations of the particles determines the crystallization of the colloidal system. The results can help us understand the underlying mechanisms of electromagnetic colloidal systems' phase transitions and to fabricate colloidal crystals.

This paper reports on the Fourth Meeting on Lorentz and CPT Symmetry, CPT '07, held in August 2007 in Bloomington, IN, USA. The focus is on recent tests of Lorentz symmetry using atomic and optical physics. Results presented at the meeting include improved bounds on Lorentz violation in the photon sector, and the first bounds on several coefficients in the gravity sector.

A detailed analysis of the intermolecular interactions in some prototype systems involving rare gas atoms and closed shell ions is presented. Through this analysis, we assess the effectiveness of a model potential recently proposed as an improvement of the Lennard-Jones' one. This has been suggested on the basis of recently available experimental and theoretical information on non-covalent intermolecular interactions. The investigation is extended to systems involving H₂O and H₂S molecules and also to hydrogen halide di-cations HX²⁺ (X=F, Cl, Br and I), wherein chemical contributions, essentially charge transfer, are added to the non-covalent components to a varied and interesting phenomenology determined which is possible to be represented within a single unified picture.

Beam–foil spectroscopy after 45 years: what has been realized of the promises? What is the state of the art? What is the status of the field? What present atomic physics problems should the technique be applied to, where can it be done? Will it be done?