Table of contents

In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann—Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established.

Here an asymptotic study to the N-dimensional radial Schrödinger equation for the quark-antiquark interaction potential employing asymptotic iteration method via an ansatz to the wavefunction is carried out. The complete energy spectra of the consigned system is obtained by computing and adding energy eigenvalues for ground state, for large "r" and for small "r". From this analysis, the mass spectra of heavy quarkonia is derived in three dimensions. Our analytical and numerical results are in good correspondence with other experimental and theoretical studies.

To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.

The work deficit, as introduced by Jonathan Oppenheim et al. [Phys. Rev. Lett. 89 (2002) 180402] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.

By analyzing the basic properties of unitary transformations used in a quantum secure direct communication (QSDC) protocol, we show the main idea why a covert channel can be established within any QSDC channel which employs unitary transformations to encode information. On the basis of the fact that the unitary transformations used in a QSDC protocol are secret and independent, a novel quantum covert channel protocol is proposed to transfer secret messages with unconditional security. The performance, including the imperceptibility, capacity and security of the proposed protocol are analyzed in detail.

We propose a tripartite scheme for probabilistically teleporting an arbitrary two-qubit state with a four-qubit cluster-class state and a Bell-class state as the quantum channels. In the scheme, the sender and the controller make Bell-state measurements (BSMs) on their respective qubit pairs. With their measurement results, the receiver can reconstruct the original state probabilistically by introducing two auxiliary particles and making appropriate unitary operations and positive operator-valued measure (POVM) instead of usual projective measurement. Moreover, the total success probability and classical communication cost of the present protocol are also worked out.

We propose an experimentally feasible protocol for implementing controlled dense coding with a six-atom cluster state in cavity QED. In the scheme, we investigate that the atoms interact simultaneously with the highly detuned single-mode cavity and the strong classical driving field, and thus our scheme is not sensitive to both the cavity decay and the thermal field. In addition, the four-atom entangled states can be exactly distinguished by performing the single-atom measurements in cavity QED, therefore our scheme might be implemented in a simple way.

We study the open quantum random walk (OQRW) with time-dependence on the one-dimensional lattice space and obtain the associated limit distribution. As an application we study the return probability of the OQRW. We also ask, "What is the average time for the return probability of the OQRW?"

Recently, deterministic joint remote state preparation (JRSP) schemes have been proposed to achieve 100% success probability. In this paper, we propose a new version of deterministic JRSP scheme of an arbitrary two-qubit state by using the six-qubit cluster state as shared quantum resource. Compared with previous schemes, our scheme has high efficiency since less quantum resource is required, some additional unitary operations and measurements are unnecessary. We point out that the existing two types of deterministic JRSP schemes based on GHZ states and EPR pairs are equivalent.

In this paper, by means of the potential systems of the given nonlinear evolution equations, a procedure of symmetry preserving discretization of differential equations is presented. The specific process will be given detailed in section 2. This extended method is effective for discreting the high-order (high-dimensional) nonlinear evolution equations. As examples, the invariant difference models of the mKdV equation and the Boussinesq equation are constructed.

Using the quark-like model, we have improved the existing deviation between theoretical and experimental values of magnetic dipole moment of deuteron. Based upon Pauli Exclusion Principle, the constituent quarks form a ground state for l = 0. The expectation value of the deuteron magnetic dipole moment operator is determined to be equal to 0.861 597 8μ_N in better agreement with the measured value of 0.857 437 6μ_N as compared to the shell model calculations.

The escape of particles in an open square-shaped cavity has been examined. We consider a family of trajectories launched from the left bottom lead of the square cavity and escaped from the right boundary. For each escaping trajectories, we record the propagation time and the detector position. We find that the escape time graph exhibits a regular sawtooth structure. For a set of detector points, we search for the classical trajectories from the source point to the detector points. Then we use semiclassical theory to construct the wave function at different given points. The calculation results suggest that the escape probability density depends on the detector position and the momentum of the particle sensitively. The Fourier transform of the semiclassical wave function gives the path length spectrum. Each peak in the path length spectrum corresponds to the length of one escape trajectory of the particle. We hope that our results will be useful in understanding the escape and transport process of particles inside a microcavity.

The structural, electronic and lattice-dynamical properties of the intermetallic Al₂Au at different electronic temperatures have been investigated via density functional calculations. The results of electronic density of state indicate that, although its value changes considerably, Al₂Au is still of metal with the increasing of electronic temperature. The acoustic mode of Al₂Au gets negative which leads to lattice dynamical instability when the electronic temperature is beyond 1.44 eV. Moreover, with the increasing of the electronic temperature, the vibrational frequencies of the T_1u optical mode (triply degenerate) of Al₂Au at Γ point decrease first and increase then, the turning point is at T_e = 1.40 eV. T_2g optical mode at Γ point has a similar situation, but the turning point is at T_e = 1.80 eV. The predicted melting temperatures of Al₂Au undergo a sharp decrease from 1333K at normal temperature to 1172 K at T_e = 1.8 eV after intense laser irradiation.

We investigate the features of the spontaneous emission spectra in a cold five-level atomic system coupled by a single elliptically polarized control field. We use wave function approach to derive the explicit and analytical expressions of atomic spontaneous emission spectra. It is shown that some interesting phenomena such as spectral-line enhancement, spectral-line suppression, spectral-line narrowing, spectral-line splitting and dark fluorescence can be observed in the spectra by appropriately modulating the phase difference between the right-hand circularly (LHC) and left-hand circularly (RHC) polarized components of the elliptically polarized control field and the intensity of external magnetic field. The number of emission peaks, the positions of fluorescence-quenching points can be also controlled. Furthermore, we propose an ultracold ⁸⁷Rb atomic system for experimental observation. These investigations may find applications in high-precision spectroscopy.

Manipulation of spontaneous emission from an atom confined in three kinds of modified reservoirs has been investigated by means of an elliptically polarized laser field. Some interesting phenomena such as the multi-peak structure, extreme spectral narrowing, and cancellation of spontaneous emission can be observed by adjusting controllable system parameters. Moreover, these phenomena depend on the constructive or destructive quantum interference between multiple decay channels and which can be changed appreciably by varying the phase difference between the two circularly polarized components of the probe field. These results demonstrate the importance of an elliptically polarized laser field in controlling the spontaneous emission and its potential applications in high-precision spectroscopy.

Analytical solutions are presented using method of separation of variables for the time periodic electroosmotic flow (EOF) of linear viscoelastic fluids in semicircular microchannel. The linear viscoelastic fluids used here are described by the general Maxwell model. The solution involves analytically solving the linearized Poisson—Boltzmann (P-B) equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influences of electric oscillating Reynolds number Re and Deborah number De on velocity amplitude are presented. For small Re, results show that the larger velocity amplitude is confined to the region near the charged wall when De is small. With the increase of the Deborah number De, the velocity far away the charged wall becomes larger for large Deborah number De. However, for larger Re, the oscillating characteristic of the velocity amplitude occurs and becomes significant with the increase of De, especially for larger Deborah number.

Using molecular dynamics simulation, we compared evaporation behavior of a tiny amount of water molecules adsorbed on solid surfaces with different dipole lengths, including surface dipole lengths of 1 fold, 2 folds, 4 folds, 6 folds and 8 folds of 0.14 nm and different charges from 0.1e to 0.9e. Surfaces with short dipole lengths (1-fold system) can always maintain hydrophobic character and the evaporation speeds are not influenced, whether the surface charges are enhanced or weakened; but when surface dipole lengths get to 8 folds, surfaces become more hydrophilic as the surface charge increases, and the evaporation speeds increase gradually and monotonically. By tuning dipole lengths from 1-fold to 8-fold systems, we confirmed non-monotonic variation of the evaporation flux (first increases, then decreases) in 4 fold system with charges (0.1e–0.7e), reported in our previous paper [S. Wang, et al., J. Phys. Chem. B 116 (2012) 13863], and also show the process from the enhancement of this unexpected non-monotonic variation to its vanishment with surface dipole lengths increasing. Herein, we demonstrated two key factors to influence the evaporation flux of a tiny amount of water molecules adsorbed on solid surfaces: the exposed surficial area of water aggregation from where the water molecules can evaporate directly and the attraction potential from the substrate hindering the evaporation. In addition, more interestingly, we showed extra steric effect of surface dipoles on further increase of evaporation flux for 2-folds, 4-folds, 6-folds and 8-folds systems with charges around larger than 0.7e. (The steric effect is first reported by parts of our authors [C. Wang, et al., Sci. Rep. 2 (2012) 358]). This study presents a complete physical picture of the influence of surface dipole lengths on the evaporation behavior of the adsorbed tiny amount of water.

We study Bose—Einstein condensation in a linear trap with a dimple potential where we model dimple potentials by Dirac δ function. Attractive and repulsive dimple potentials are taken into account. This model allows simple, explicit numerical and analytical investigations of noninteracting gases. Thus, the Schrödinger equation is used instead of the Gross—Pitaevski equation. We calculate the atomic density, the chemical potential, the critical temperature and the condensate fraction. The role of the relative depth of the dimple potential with respect to the linear trap in large condensate formation at enhanced temperatures is clearly revealed. Moreover, we also present a semi-classical method for calculating various quantities such as entropy analytically. Moreover, we compare the results of this paper with the results of a previous paper in which the harmonic trap with a dimple potential in 1D is investigated.

The two-electron Hooke's atom — a quantum mechanical system with two electrons bound in a harmonic potential — is well known for its exact analytical properties at certain oscillator strengths. The Hooke's atoms with more than two electrons offer more scope for valuable practical applications. In this work, we study the asymptotic structure of these Hooke's atoms in the classically forbidden region. The leading-order term of the long-range expression for the KS exchange-correlation potential v_xc(r) is shown to be −1/r. The second and third higher order terms are also exactly obtained. Various components of v_xc(r) are also studied. It is shown that the leading term of O(1/r) in v_xc(r) is due to the pure Pauli correlation, while the leading contribution of the Coulomb correlation is of O(1/r³). Neither of them makes contribution to the term of O(1/r²), which is shown to be solely due to the kinetic correlation effect. Results for the two-electron Hooke's atom were obtained before in the literature. Our results reduce to those of the two-electron Hooke's atom as a special case.

The dynamical self-trapping of an excitation propagating on one-dimensional of different sizes with next-nearest neighbor (NNN) interaction is studied by means of an explicit fourth order symplectic integrator. Using localized initial conditions, the time-averaged occupation probability of the initial site is investigated which is a function of the degree of nonlinearity and the linear coupling strengths. The self-trapping transition occurs at larger values of the nonlinearity parameter as the NNN coupling strength of the lattice increases for fixed size. Furthermore, given NNN coupling strength, the self-trapping properties for different sizes are considered which are some different from the case with general nearest neighbor (NN) interaction.

The effect of terminal groups on the electron transport through metal-molecule-metal system has been investigated using nonequilibrium Green's function (NEGF) formalism combined with extended Huckel theory (EHT). Au-molecule-Au junctions are constructed with borazine and BCN unit structure as core molecule and sulphur (S), oxygen (O), selenium (Se) and cyano-group (CN) as terminal groups. The electron transport characteristics of the borazine and BCN molecular systems are analyzed through the transmission spectra and the current-voltage curve. The results demonstrate that the terminal groups modifying the transport behaviors of these systems in a controlled way. Our result shows that, selenium is the best linker to couple borazine to Au electrode and oxygen is the best one to couple BCN to Au electrode. Furthermore, the results of borazine systems are compared with that of BCN molecular systems and are discussed. Simulation results show that the conductance through BCN molecular systems is four times larger than the borazine molecular systems. Negative differential resistance behavior is observed with borazine-CN system and the saturation feature appears in BCN systems.

In the present work, the entropy and internal energy of a GaAs cylindrical quantum dot in the presence of an applied magnetic field is studied. For this purpose, the Tsallis formalism is applied to obtain internal energy and entropy. It is found that entropy and internal energy are continuous function and they are zero at special temperatures. Entropy maximum increases with increasing dot radius. Internal energy increases by increasing magnetic field.