Close to converged energies and wave functions for the positron binding systems, LiPs and $e^+$Be are computed using the stochastic variational method. Binding energies and annihilation rates from both $ab$-$initio$ and fixed core calculations are determined and found to be in agreement. The $ab$-$initio$ binding energy of $e^+$Be was 0.00316 Hartree while that for LiPs was 0.01237 Hartree.

We discuss the blinking statistical behaviors of dynamics of single molecule system, using the recently developed generating function method. We make a thorough study of the fluorescence blinking behaviors and get the statistical properties of the jumping events respectively onto ON state or OFF state, such as the waiting time and waiting time distribution for every directional jumping event, the cumulants of jumping events, the cross correlation, the joint probabilities between two directional jumping events and the probabilities.

Adsorption studies of $Cs^+$, $Tl^+$, $Sr^{2+}$ and $Co^{2+}$ on activated carbons from aqueous solutions are reported. The carbon samples were characterized using different techniques. The chemical nature of the surface of the activated carbon was studied. Optimal conditions for adsorption of the metal ions have been identified. The comparative study for the metal ions was also considered in the presence of different anions. The data suggest the possible use of activated carbons for preconcentration and separation of some cations.

In this communication, studies of the total ionization cross sections of hydrocarbon molecules ($CH,$ $C_2H_2$) due to electron impact are presented. Electron impact ionization cross sections (EIICS) have been calculated from threshold ionization energy to high energy (10 MeV). Apart from EIICS calculation the values of collisional parameters are also calculated. The theoretical model, developed by Khare, has been modified to calculate the total ionization cross section for molecules. Obtained theoretical cross sections are compared extensively with a number of experimental and theoretical data. The obtained values of collisional parameter compared with the available experimental values.

High-order correction terms to the expression of the field of circularly polarized Gaussian laser are derived. Terms up to seventh order in the small dimensionless spatial parameter are explicitly presented. Using the test particle simulation programs, the CAS (Capture & Acceleration Scenario) phenomenon in the circularly polarized field has been proved, and the difference efficiency of CAS scheme between the circularly polarized field and linearly polarized field has been investigated, further more the electron dynamics obtained by the paraxial approximation, the fifth-order correction, and the seventh-order correction are compared in detail. The numerical calculations show that the results of three corrected models coincide with each other very well for $kw_{0}> 60$, and the difference of the three corrected models is very conspicuously for $kw_{0}\leq 50$. Then the ranges of the electron incident momentum for the CAS scheme in circularly polarized field to emerge are examined. This study is of significance in designing experimental setup to test CAS and helpful in understanding the basic physics of CAS.

The conductance of carbon atomic wire in the environment of $H_2O$ molecules is studied by the non-equilibrium Green function method  based on density functional theory. In particular,  the carbon wire with seven atoms sandwiched between the Al(100) electrodes is considered. It is found that the transport properties are sensitive to the variation of the number and the position of the $H_2O$ molecule adsorbed on the carbon wire. To our surprise, with different positions of a single $H_2O$ molecule on the carbon wire, the equilibrium conductance shows an evident odd-even oscillatory behavior. For example, the equilibrium conductance  of the  carbon wire becomes bigger when the $H_2O$ is adsorbed on the odd-numbered carbon atoms; an opposite conclusion is obtained for the $H_2O$ adsorbed on the even-numbered carbon atoms. For the cases of two $H_2O$ molecules, the equilibrium conductance varies largely and the contribution of the third eigenchannel becomes larger in some special configurations. The above behavior is analyzed via the charge transfer and the density of states (DOS). Reasonable explanations are presented.

A quantum stationary wave has been examined in an exchange field, which induces the force of the form $F(r)=f_{2}(1/r^{2}-f_{1}/r)$. For the Coulomb attraction in hydrogen atom, the inexplicable discrepancy (0.0023 MHz) between the theoretical and experimental frequencies for its $^{1}S_{1/2}$ has been verified. It is found that the tiny $f_{1}$ is $7.45\times10^{-12}a_{1}$$^{-1}$($a_{1}$ is the 1st Bohr radius). Meanwhile, when such an $f_{1}$ is considered in the $n=2$ Lamb shift, it causes -0.034 MHz difference, which is in good agreement with the deviation of -0.039 MHz between the experimental and one of the theoretical predictions. Similar of searchings are made for the Lande $g$ factor for the $H_{\beta}$ spectrum. This $f_{1}$ contributes a ratio $\Delta g/g=5.58\times10^{-11}$ and makes both the experiment and theory well agreed within the experimental relative uncertainty $\pm4\times10^{-12}$. In other words, these phenomena can be treated as the reliable physical evidences for the existence of the same repulsion. More importantly, they consistently and strongly imply that the maximum radius for the Coulomb attraction in hydrogen atom can not exceed 7.11$m$ (if extrapolated). In addition, this analysis prompts us similar cases probably occur in the gravitation because it is also an exchange field, and the repulsion at remote distance may be one kind of dark energy that may have been ignored.

We theoretically examine thickness and wavelength dependence line-shape of four-wave-mixing (FWM) spectroscopy in micrometric thin atomic vapors whose thickness $L$ is assumed to be 10,30,50,80 and 100 $\mu$m respectively. It is found that a narrow centre (Dicke-narrowing) persists for all cases, while wings are broadened as the thickness of the vapor increases or the pump wavelength decreases comparing to the probe wavelength. This type of spectrum is due to the modified velocity distribution and polarization interference from different ensemble of atoms in a confined situation.

A scheme is presented for remote state preparation of three-particle GHZ-class states by using a Bell state and an asymmetric W state as the quantum channel. In the scheme, the success probability of preparation and classical communication cost are calculated. In general, Bob can successfully prepare the initial state with the probability 1/4 and consume 1/4 classical bits. However, in special situations the success probability of preparation can reach 1/2 or even 1 after consuming a little additional classical bits.

I present a novel tripartite scheme for remotely preparing an arbitrary two-qubit state with two three-qubit entanglements. By using a proper positive operator-valued measure (POVM), it is shown the remote two-qubit preparation can be realized in either distant ministrant's place in a probabilistic manner via their collaboration. I also explore its applications to six special ensembles of state in detail. The extensive investigations shows that the remote preparation can be achieved with higher probability provided that the prepared state belongs to the six special ensembles.