Quantum Entanglement of Two Atoms Inside an Optical Cavity

We investigate the system,which consists of two two-level atoms confined in a linear trap which has been surrounded by an optical cavity,with the Milburn model of intrinsic decoherence,and find an explicit analytical solution of the Milburn equation.the entanglement between the two atoms is then calculated by making use of concurrence.The influence of intrinsic decoherence on the entanglement is also discussed.     

Influence of Intrinsic Decoherence on Nonclassical Effects of System of a Three-Level Atom in Ξ Configuration

With the help of an SU(3) dynamical algebraic structure, we find an exact solution of the Milburn equation for the system of a three-level atom in the Ξ configuration interacting with one quantized field mode with arbitrary detuning. The exact solution is then used to discuss the influence of the intrinsic decoherence on the nonclassical properties of the system, such as collapes and revivals of the atomic populations, oscillations of the photon number distribution, and squeezing of the radiation field.     

Symmetry Analysis of Two Types of （2＋1）-Dimensional Nonlinear Klein-Gorden Equation

By means of the classical symmetry method, we investigate two types of the （2＋1）-dimensional nonlinear Klein-Gorden equation. For the wave equation, we give out its symmetry group analysis in detail. For the second type of the （2＋1）-dimensional nonlinear Klein-Gorden equation, an optimal system of its one-dimensional subalgebras is constructed and some corresponding two-dimensional symmetry reductions are obtained.     

Abundant Symmetries and Exact Compacton—Like Structures in the Two—Parameter Family of the Estevez—Mansfield—Clarkson Equations

The two-parameter family of Estevez-Mansfield-Clarkson equations with fully nonlinear dispersion (called E(m,n) equations),(uz^m)zzτ γ(uz^nuτ)z uττ=0 which is a generalized model of the integrable Estevez-Mansfield-Clarkson equation uzzzτ γ(uzuzτ uzzuτ) uττ=0,is presented.Five types of symmetries of the E9m,n) equation are obtained by making use of the direct reduction method.Using these obtained reductions and some simple transformations,we obtain the solitary-like wave solutions of E(1,n) equation.In addition,we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions,they reemerge with the same coherent shape) of E(3,2) equation and E(m,m-1) for its potentials,say,uz,and compacton-like solutions of E(m,m-1) equations,respectively.Whether there exist compacton-like solutions of the other E(m,n) equation with m≠n 1 is still an open problem.     

Influence of Intrinsic Decoherence on Nonclassical Effects of System of a Three-LevelAtom in [1] Configuration

With the help of an SU(3) dynamicalalgebraic structure, we ~nd an exact solutionof the Milburn equationfor the system of a three-levelatom in the [1] configuration interacting with one quantized field mode with arbitrary detuning ,The exact solution is then used to discuss the influence of the intrinsic decoherence on the nonclassical properties of the system,such as collapes and revivals of the atomic populations,oscillations of the photon number distribution,and squeezing of the radiation field.     

large Last Multiplier of Generalized Hamilton System

We study an application of the Jacobi last multiplier to a generalized Hamilton system. A partial differential equation on the last multiplier of the system is established. The last multiplier can be found by the equation. If the quantity of integrals of the system is sufficient, the solution of the system can be found by the last multiplier.     

On the fundamental equation of nonequilibrium statistical physics—Nonequilibrium entropy evolution equation and the formula for entropy production rate

In this paper the author presents an overview on his own research works. More than ten years ago, we proposed a new fundamental equation of nonequilibrium statistical physics in place of the present Liouville equation. That is the stochastic velocity type’s Langevin equation in 6N dimensional phase space or its equivalent Liouville diffusion equation. This equation is time-reversed asymmetrical. It shows that the form of motion of particles in statistical thermodynamic systems has the drift-diffusion duality, and the law of motion of statistical thermodynamics is expressed by a superposition of both the law of dynamics and the stochastic velocity and possesses both determinism and probability. Hence it is different from the law of motion of particles in dynamical systems. The stochastic diffusion motion of the particles is the microscopic origin of macroscopic irreversibility. Starting from this fundamental equation the BBGKY diffusion equation hierarchy, the Boltzmann collision diffusion equation, the hydrodynamic equations such as the mass drift-diffusion equation, the Navier-Stokes equation and the thermal conductivity equation have been derived and presented here. What is more important, we first constructed a nonlinear evolution equation of nonequilibrium entropy density in 6N, 6 and 3 dimensional phase space, predicted the existence of entropy diffusion. This entropy evolution equation plays a leading role in nonequilibrium entropy theory, it reveals that the time rate of change of nonequilibrium entropy density originates together from its drift, diffusion and production in space. From this evolution equation, we presented a formula for entropy production rate (i.e. the law of entropy increase) in 6N and 6 dimensional phase space, proved that internal attractive force in nonequilibrium system can result in entropy decrease while internal repulsive force leads to another entropy increase, and derived a common expression for this entropy decrease rate or another entropy increase rate, obtained a theoretical expression for unifying thermodynamic degradation and self-organizing evolution, and revealed that the entropy diffusion mechanism caused the system to approach to equilibrium. As application, we used these entropy formulas in calculating and discussing some actual physical topics in the nonequilibrium and stationary states. All these derivations and results are unified and rigorous from the new fundamental equation without adding any extra new assumption.     

Size-dependent thermal stresses in the core–shell nanoparticles

The thermal stress in a magnetic core–shell nanoparticle during a thermal process is an important parameter to be known and controlled in the magnetization process of the core–shell system. In this paper we analyze the stress that appears in a core–shell nanoparticle subjected to a cooling process. The external surface temperature of the system, considered in equilibrium at room temperature, is instantly reduced to a target temperature. The thermal evolution of the system in time and the induced stress are studied using an analytical model based on a time-dependent heat conduction equation and a differential displacement equation in the formalism of elastic displacements. The source of internal stress is the difference in contraction between core and shell materials due to the temperature change. The thermal stress decreases in time and is minimized when the system reaches the thermal equilibrium. The radial and azimuthal stress components depend on system geometry, material properties, and initial and final temperatures. The magnitude of the stress changes the magnetic state of the core–shell system. For some materials, the values of the thermal stresses are larger than their specific elastic limits and the materials begin to deform plastically in the cooling process. The presence of the induced anisotropy due to the plastic deformation modifies the magnetic domain structure and the magnetic behavior of the system.     

Some dynamical property of the Tsallis distribution from a Fokker-Planck equation

This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.     

The classification of travelling wave solutions and superposition of multi-solutions to Camassa-- Holm equation with dispersion

Under the travelling wave transformation, the Camassa--Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa--Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa--Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa--Holm equation with dispersion.     

Exact Solution of the Milburn Equation for the Coupled-Channel Cavity QED Model

We give the exact solution of Milburn equation for a coupled-channel cavity QED model which includes the Stark term and the frequency detuning, and study the influence of the intrinsic decoherence on the atomic inversion of the system.     

The Exact Solution of Milburn Equation Without Diffusion Approximation for the Two-Model Raman Coupled Model

By making use of the dynamical algebraic approach, we study the two-mode Raman coupled model governed by the Milburn equation and find the exact solution of the Milburn equation without diffusion approximation. The exact solution is then used to discuss the influence of intrinsic decoherence on the revivals of atomic inversion, oscillation of the photon number distribution and squeezing of radiation field in the whole ranges of the decoherence parameter γ.     

Effect of Intrinsic Decoherence on Nonclassical Effects of the Nondegenerate Bimodal Multiquanta JCM

We study the nondegenerate multiquanta Jaynes-Cummings model governed by Milburn equation. This models the decoherence of a quantum system as it evolves through intrinsic mechanisms beyond conventional quantum mechanics governed by the Schrödinger equation. We find an exact solution of this equation and apply it to investigate the effects of the intrinsic decoherence on nonclassical effects of the system, such as collapses and revivals of the population inversion and squeezing of the radiation field, for the resonant and the off-resonant cases when the particle (atom or trapped ion) is taken to be prepared initially in a coherent superposition state.     

Influence of Intrinsic Decoherence in the Presence of Stark Shift on Nonclassical Properties of the Two-Mode JCM

We study the influence of intrinsic decoherence in the presence of Stark shift for the two-mode Jaynes—Cummings model (JCM). An analytic solution of the Milburn equation for the multiquant two-mode JCM Hamiltonian is obtained. We use this solution to investigate the influence of intrinsic decoherence and Stark shift on nonclassical properties of the system, for the resonant and the off-resonant cases. We compare the behavior of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field.     

双模场与原子相互作用中的量子纠缠和内禀退相干

通过求解系统的Milburn方程，研究了两能级原子与双模SU(1,1)相干态光场发生相互作用系统中，原子与场的纠缠及双模SU(1,1)相干态场的模间纠缠随时间的演化问题，讨论了内禀退相干、双模光子数差等对纠缠度的影响.结果表明，存在内禀退相干时，随着时间的演化，场-原子纠缠逐渐减小到一个确定值，而模间纠缠逐渐增大到一个确定值，两者演化的最终值只取决于双模光子数差和平均光子数，而与内禀退相干因子无关. 关键词： Milburn理论 SU(1 1)相干态 量子约化熵 量子相对熵     

Intrinsic decoherence of entanglement of a single quantized field interacting with a two-level atom

How the mean photon number, the probability of excited state and intrinsic decoherenee coefficient in-fluence the time evolution of entanglement is unknown, when a single-mode quantized optic field and a two-levelatom coupling system is governed by Milburn equation. The Jaynes-Cummings model is considered. A lowerhound of concurrence is proposed to calculate the entanglement. Simulation results indicate that the entanglementof system increases following the increasing of intrinsic decoherence coefficient or the decreasing of the mean photon number. Besides that, the entanglement of system decreases, while the probability of exited state increasesfrom 0 to 0.1, and increases, while the probability of exited state increases from 0.1 to 1.     

Entropy Squeezing in Coupled Field-Superconducting Charge Qubit with Intrinsic Decoherence

We investigate the entropy squeezing in the system of a superconducting charge qubit coupled to a single mode field. We find an exact solution of the Milburn equation for the system and discuss the influence of intrinsic decoherence on entropy squeezing. As a comparison, we also consider the variance squeezing. Our results show that in the absence of the intrinsic decoherence both entropy and variance squeezings have the same periodic properties of time, and occur at the same range of time. However, when the intrinsic decoherence is considered, we find that as the time going on the entropy squeezing disappears fast than the variance squeezing, there exists a range of time where entropy squeezing can occur but variance squeezing cannot.     

Intrinsic decoherence of entanglement of a single quantized field interacting with atwo-level atom

How the mean photon number, the probability of excited state and intrinsic decoherence coefficient influence the time evolution of entanglement is unknown, when a single-mode quantized optic field and a two-level atom coupling system is governed by Milburn equation. The Jaynes-Cummings model is considered. A lower bound of concurrence is proposed to calculate the entanglement. Simulation results indicate that the entanglement of system increases following the increasing of intrinsic decoherence coefficient or the decreasing of the mean photon number. Besides that, the entanglement of system decreases, while the probability of exited state increases from 0 to 0.1, and increases, while the probability of exited state increases from 0.1 to 1.     

Entropy Squeezing in Coupled Field-Superconducting Charge Qubit with Intrinsic Decoherence

We investigate the entropy squeezing in the system of a superconducting charge qubit coupled to a single mode field. We find an exact solution of the Milburn equation for the system and discuss the influence of intrinsic decoherence on entropy squeezing. As a comparison, we also consider the variance squeezing. Our results show that in the absence of the intrinsic decoherence both entropy and variance squeezings have the same periodic properties of time,and occur at the same range of time. However, when the intrinsic decoherence is considered, we find that as the time going on the entropy squeezing disappears fast than the variance squeezing, there exists a range of time where entropy squeezing can occur but variance squeezing cannot.