Regularization as Quantization in Reducible Representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials (an alternative to the Gupta-Bleuler method) is tested on the example of quantum electromagnetic fields produced by a classical current. The Heisenberg dynamics can be consistently formulated since the fields are given by operators and not operator-valued distributions. The scheme involves a Hamiltonian whose free part is modified but the minimal-coupling interaction is the standard one. Solving Heisenberg equations of motion under the assumption that the fields are free for times t ₀ = ±∞ we arrive at retarded and advanced solutions. Once we have these solutions we can deduce the form of evolution of retarded and advanced fields between two arbitrary finite times. The appropriate unitary evolution operators are found and their generators are computed. Now the generators involve the same free part as before, but the interaction term turns out to be modified. For a pointlike charge localized on a world-line z ^a (t) we find the interaction term of the form where the integration is along those parts of the charge world-line where the charge velocity is nonzero. There is no self-energy contribution. Next we compute photon statistics. Poisson statistics naturally results and infrared divergence can be avoided even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincaré covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to Rényi’s α. It is shown that the “Shannon limit” α→ 1 plays here a role of a correspondence principle with the standard regularized formalism. PACS: 03.70.+k, 41.20.Jb, 42.50.-p.     

Generation of a four-qubit cluster state for atoms in a thermal cavity

We propose two schemes for generating a four-atom cluster state in a thermal cavity. With the assistant of a strong classical field the photon-number-dependent parts in the effective Hamiltonian are canceled. Thus the schemes are insensitive to the thermal field. The schemes can also be used to generate the cluster state for the trapped ions in thermal motion.     

Structure of Rotating Neutron Stars in Uniform Strong Magnetic Field

Properties and deformations of the rotating neutron stars in uniform strong magnetic field are calculated. The magnetic field will soften the equation of state of the neutron star matters and make an obvious effect on the structure of the rotating neutron star. If the magnetic field is superstrong （B=10^17 T）, the mass, radius, and the deformation will become smaller effectively.     

Exploring Microstructures and Interphase Properties of Surface- Grafted Diblock Copolymers in a Homopolymer Melt by Self-Consistent Field Theory Simulations

Polymeric self-consistent field theory is used to investigate microstructures and interphase properties of diblock copolymers grafted onto solid surfaces in a homopolymer melt. The calculations show that the grafted diblock copolymers can self-assemble into hemispherical microstructures at low grafting densities of the diblock copolymers. The morphology transforms into hemicylinder-like and sandwich-like lamellar microstructures with an increase in the chain-grafting density. The effective thickness of the grafted block layer and the interphase width between the homopolymer melt and the grafted copolymers strongly depend on the physicochemical parameters of the system, such as the composition of the grafted copolymer, the chemical incompatibility between the different components, the length ratio of grafted copolymer to homopolymer, and the grafting density of the diblock copolymers. In addition, the above computational results of microphase-separated structures and interphase properties are qualitatively compared with our previous experimental observations. The comparison indicates that our theoretical results not only reproduce the general feature of the experimental observations, but also elucidate the internal structural information and complement the findings in the region of high grafting densities of diblock copolymers.     

新颖的高温流场红外辐射物性参数计算方法

为解决高速飞行器红外辐射特性研究中高温气体辐射参数计算问题,在转动平滑谱带（smeared rotational band, SRB）模型的假设下,首次提出基于贝叶斯估计的跳转马尔科夫链蒙特卡罗（reversible jump Markov chain monte carlo, RJMCMC）方法来计算高温流场中气体组分红外光谱物性参数。仿真计算和实验测量表明,仅需很少的先验知识,且不需要相关跃迁系数,该方法可以很好的估计主要振动跃迁带的位置,所提取的SRB模型参数的变化规律与SRB理论模型结果一致,利用拟合参数计算得到不同温度下谱带积分发射和吸收系数与逐线计算的结果非常近似。     

Nonlinear phase field theory for fracture and twinning with analysis of simple shear

A phase field theory for coupled twinning and fracture in single crystal domains is developed. Distinct order parameters denote twinned and fractured domains, finite strains are addressed and elastic nonlinearity is included via a neo-Hookean strain energy potential. The governing equations and boundary conditions are derived; an incremental energy minimization approach is advocated for prediction of equilibrium microstructural morphologies under quasi-static loading protocols. Aspects of the theory are analysed in detail for a material element undergoing simple shear deformation. Exact analytical and/or one-dimensional numerical solutions are obtained in dimensionless form for stress states, stability criteria and order parameter profiles at localized fractures or twinning zones. For sufficient applied strain, the relative likelihood of localized twinning vs. localized fracture is found to depend only on the ratio of twin boundary surface energy to fracture surface energy. Predicted criteria for shear stress-driven fracture or twinning are often found to be in closer agreement with test data for several types of real crystals than those based on the concept of theoretical strength.     

DYNAMICS of H+2 in TWO-COLOR ULTRASHORT LASER PULSE

Numerical simulations of ionization and dissociation processes of hydrogen molecular ion H₂⁺ interacting with two-color intense ( 10¹⁴W/cm²-10¹⁵W/cm²) ultrashort (the duration ≈ 22fs) laser pulse are made. The result shows that the ionization and dissociation processes are strongly dependent upon the relative phase between the two color fields. It means that, in the case of ultrashort pulse, the phase coherence control of ionization and dissociation processes can be realized.     

Radiation-induced fermion resonance

The Dirac equation is solved for two novel terms which describe the interaction energy between the half-integral spin of a fermion and the classical, circularly polarized, electromagnetic field. A simple experiment is suggested to test the new terms and the existence of radiation-induced fermion resonance.     

Quantum theory of rotation angles: The problem of angle sum and angle difference

We reconsider the problem of the sum and difference of two angle variables in quantum mechanics. The spectra of the sum and difference operators have widths of , but angles differing by are indistinguishable. This means that the angle sum and difference probability distributions must be cast into a range. We obtain probability distributions for the angle sum and difference and relate this problem to the representation of nonbijective canonical transformations. Received: 6 December 1997 / Revised: 15 April 1998 / Accepted: 7 May 1998     

二次域Q（√7）的单位给出的三角数及相关的不定方程问题

研究了二次域Q（√7）中单位Vn＋Un√7）=（8＋3√7）n所给出的两个递归数列{Vn},{Un}中的三角数问题,找到了{Vn},{Un}中的所有的三角数.作为应用,给出了与其相关的两个不定方程的整数解.