Thermal Entanglement Between Two Two-Level Atoms in a Two-Photon Jaynes-Cummings Model with an Added Kerr Medium

In this paper, we consider a Hamiltonian model that includes interaction of two coupled two-level atoms with a single-mode quantized electromagnetic field in a cavity via the degenerate two-photon transition. The cavity is filled with a Kerr-like medium and is held at a temperature T. The free field Hamiltonian possesses the su(1,1) symmetry which realized by either even or odd photon-number states. The total number of excitation as a constant of motion, provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a results, the representation of the Hamiltonian becomes block-diagonal matrix with three blocks. After diagonalizing each block, we obtain thermal state of system in the whole Hilbert space and within its excitation subspaces. Finally, the effect of temperature, atom-atom and Kerr-type couplings on the degree of thermal entanglement between the atoms are investigated. Our results show that within the single-excitation subspace spanned with odd photon-number states, the entanglement between the atoms is thermally robust.     

Soliton solutions and stability analysis for some conformable nonlinear partial differential equations in mathematical physics

This research presents soliton solutions and stability analysis to some conformable nonlinear partial differential equations (CNPDEs). The CNPDEs equations in this paper are conformable Cahn–Allen and conformable Zoomeron equations. The powerful sine-Gordon method is used to carry out the soliton solutions for these equations. The aspects of stability analysis for the considered equations is investigated using the linear stability technique. The sine-Gordon method proves to be efficient and effective for the extraction of soliton solutions for different types of CNPDEs.     

Lie symmetry analysis and explicit solutions for the time fractional generalized Burgers–Huxley equation

Optical and Quantum Electronics - Investigated in this paper is the modified Hirota equation with variable coefficients, which can describe the amplification or absorption of pulses propagating in...     

Empirical formulas for proton decay half-lives:Role of nuclear deformation and Q-value

Two empirical formulas for the proton decay half-lives including nuclear deformation are proposed. The formula with parameter set I gives the logarithm of the proton decay half-lives as an explicit function of the orbital angular momentum with eight adjustable parameters, whereas that with set II represents the logarithm of the reduced half-lives as an implicit function of the angular momentum with seven adjustable parameters. Experimental data for the half-lives of 44 proton emitters in the ground state or isomeric state were used to obtain the parameters. The experimental and calculated Q values were used. Different sets of parameters were obtained for the ground state transition, isomeric state transition, and all transitions for both deformed and spherical nuclei. The best agreement with experimental data was observed for set I for deformed proton emitters with experimental Q values.     

Modified equation of state for pure and hard sphere mixtures in mean ionic activity coefficient calculations by mean spherical approximation model

A hard sphere equation of state (EOS) based on tetrakaidecahedron cell geometry (instead of spherical shape) and highly optimized molecular dynamic simulation data is proposed. The EOS is extended to hard sphere mixture and its performance for compressibility factor calculation at different diameter size of hard sphere mixtures by using various mixing rule is compared with Monte Carlo simulation data. The results indicated that for all mixing rules, the proposed EOS has minimum error comparing with computer simulation data. Also the residual prosperities are derived by using the proposed EOS. The residual properties are used in mean spherical approximation model (MSA) to evaluate the mean ionic activity coefficient of aqueous electrolyte solutions. The results are compared with those obtained by similar hard sphere equations of state and it is shown that the proposed EOS has a better performance in predicting the mean ionic activity coefficient.     

Magnetic strings in Einstein–Born–Infeld-dilaton gravity

A class of spinning magnetic string in 4-dimensional Einstein-dilaton gravity with Liouville type potential which produces a longitudinal nonlinear electromagnetic field is presented. These solutions have no curvature singularity and no horizon, but have a conic geometry. In these spacetimes, when the rotation parameter does not vanish, there exists an electric field, and therefore the spinning string has a net electric charge which is proportional to the rotation parameter. Although the asymptotic behavior of these solutions are neither flat nor (A)dS, we calculate the conserved quantities of these solutions by using the counterterm method. We also generalize these four-dimensional solutions to the case of (n+1)$(n+1)$-dimensional rotating solutions with k?[n/2]$k?[n/2]$ rotation parameters, and calculate the conserved quantities and electric charge of them.     

An inexact proximal regularization method for unconstrained optimization

We present a regularization algorithm to solve a smooth unconstrained minimization problem.This algorithm is suitable to solve a degenerate problem, when the Hessian is singular at a local optimal solution. The main feature of our algorithm is that it uses an outer/inner iteration scheme. We show that the algorithm has a strong global convergence property under mild assumptions. A local convergence analysis shows that the algorithm is superlinearly convergent under a local error bound condition. Some numerical experiments are reported.     

Copper(I)-Catalyzed Highly Enantioselective [3+3]-Cycloaddition of β-Aryl/Alkyl Vinyl Diazoacetates with Nitrones

β-Aryl/alkyl vinyl diazoacetates were investigated in metallo-vinylcarbene reactions with nitrones, revealing a Rh₂(OAc)₄-catalyzed cyclopropene dimerization reaction and a copper(I) catalyzed [3+3]-cycloaddition of nitrones. The chiral cyclopropyl-In-SaBox ligand with copper(I) catalysis could realize the asymmetric version of the cycloaddition reaction, delivering various 3,6-dihydro-1,2-oxazine derivatives in good yield and with excellent enantioselectivity under mild conditions.     

Surfactant‐assisted dispersive liquid–liquid microextraction of nitrazepam and lorazepam from plasma and urine samples followed by high‐performance liquid chromatography with UV analysis

Surfactant‐assisted liquid–liquid microextraction followed by high‐performance liquid chromatography with UV detection has been developed for the simultaneous preconcentration and determination of lorazepam and nitrazepam in biological fluids. In this study, an ionic surfactant (cetyltrimethyl ammonium bromide) was used as an emulsifier. The predominant parameters affecting extraction efficiency such as the type and volume of extraction solvent, the type and concentration of surfactant, sample pH, and the concentration of salt added to the sample were investigated and opted. Under the optimum conditions (extraction solvent and its volume, 1‐octanol, 70 μL; surfactant and its concentration, 1 mL of ultra‐pure water containing 2 mmol L^?1 cetyltrimethyl ammonium bromide; sample pH = 9 and salt content of 10% NaCl w/v), the preconcentration factors were obtained in the range of 202–241 and 246–265 for nitrazepam and lorazepam, respectively. The limits of quantification for both drugs were 5 μg L^?1 in water sample and 10 μg L^?1 in biological fluids with R² values higher than 0.993. The suitability of the proposed method was successfully confirmed by the extraction and determination of the target drugs in human urine and plasma samples in the range of microgram per liter.     

Observation of the "missing" polar OCS dimer

A new infrared band at 2069.3 cm-1 is observed and assigned to the long-anticipated polar isomer of the OCS dimer, helping to explain apparent discrepancies among earlier studies. The data reported here should enable direct observation of the microwave spectrum of polar (OCS)2 and motivate new theoretical works on the energetics of OCS dimer isomers and interconversion energy barriers.