Analytic Method to Study Influence of Finite Chemical Potential in QED3

Adopting the approximation to the first order of chemical potential μ, we resolve rigidly the influence on fermion condensate from μ in QED3. We show that this condensate does not respond linear expression to μ. Moreover, the influence on fermion chiral condensate from chemieal potential is investigated.     

A Modified Approach for Calculating Dressed Quark Propagator at Finite Chemical Potential

Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the full inverse quark propagator at finite chemical potential is analytic in the neighborhood of μ = 1, it is proved that the dressed quark propagator at finite chemical potential μ can be written as G0^-1 [μ] =iγ·p↑-A（p↑-^2） ＋B（p↑-^2） with p↑-μ= （p↑-p4 ＋iμ）. From the dressed quark propagator at finite chemical potential in Munczek model the bag constant of a baryon and the scalar quark condensate are evaluated. A comparison with previous results is given.     

Chemical Potential Dependence of Vertices

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential (μ=0) and neglecting the μ-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 (2005) 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ=0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 (1998) 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell-Mann-Oakes-Renner relation also holds at finite chemical potential.     

Critical Number of Fermion Flavors at Finite Chemical Potential in QED3

We propose a new method for calculating the dressed fermion propagator at finite chemical potential in QED3 under the rainbow approximation of Dyson-Schwinger equation. In the above approximation, we show that the dressed fermion propagator at finite chemical potential # has the form S（p） = iγ.p^-A（p^-2） ＋ B（ p^-2） with p^-μ= （p^-1p3 ＋ iμ）. Using this form of fermion propagator at nonzero chemical potential, we investigate the Dyson-Schwinger equation for the dressed fermion propagator at finite chemical potential and study the effects of the chemical potential on the critical number of the fermion flavors.     

Object Picture of Electromagnetic Quasinormal Ringing for a Stringy Black Hole

We investigate the evolution of an electromagnetic field in the spacetime of a stringy black hole. The object picture of the quasinormal ringing has been obtained by the finite difference method. Compared with a Schwarzschild black hole, the results show that the electromagnetic field damps more slowly for a stringy black hole.     

Dynamical Symmetry Breaking of Maximally Generalized Yang-Mills Model and Its Restoration at Finite Temperatures

In terms of the Nambu-Jona-Lasinio mechanism, dynamical breaking of gauge symmetry for the maximally generalized Vang-Mills model is investigated. The gauge symmetry behavior at finite temperature is also investigated and it is shown that the gauge symmetry broken dynamically at zero temperature can be restored at finite temperatures.     

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off A by summing the forces induced by the all fluctuation modes. We show that the Casimir force is independent of the cut-off function in the limit L∧ → ∞. There is a correction in the order of （L∧）^-2, when L∧ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale ∧^-1. It has been demonstrated that the Casimir force at a finite cut-off should be defined by summing forces of all fluctuation modes, instead of the derivative of Casimir energy with respect to L where an additional derivative of the cut-off function has been introduced.     

From Rosochatius System to KdV Equation

The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosoehatius hierarchy.     

Finite size effects on helical edge states in HgTe quantum wells with the spin orbit coupling due to bulk- and structure-inversion asymmetries

There is a quantum spin Hall state in the inverted HgTe quantum well, characterized by the topologically protected gapless helical edge states lying within the bulk gap. It has been found that for a strip of finite width, the edge states on the two sides can couple together to produce a gap in the spectrum. The phenomenon is called the finite size effect in quantum spin Hall systems. In this paper, we investigate the effects of the spin-orbit coupling due to bulk- and structure-inversion asymmetries on the finite size effect in the HgTe quantum well by means of the numerical diagonalization method. When the bulk-inversion asymmetry is taken into account, it is shown that the energy gap Eg of the edge states due to the finite size effect features an oscillating exponential decay as a function of the strip width of the HgTe quantum well. The origin of this oscillatory pattern on the exponential decay is explained. Furthermore, if the bulk- and structure-inversion asymmetries are considered simultaneously, the structure-inversion asymmetry will induce a shift of the energy gap Eg closing point. Finally, based on the roles of the bulk- and structure-inversion asymmetries on the finite size effects, a way to realize the quantum spin Hall field effect transistor is proposed.     

Fluctuation Analysis of Decoy State QKD with Finite Data-Set Size

Decoy state method quantum key distribution （QKD） is one of the promising practical solutions for BB84 QKD with coherent light pulses. The number of data-set size in practical QKD protocol is always finite, which will cause statistical fluctuations. In this paper, we apply absolutely statistical fluctuation to amend the yield and error rate of the quantum state. The relationship between exchanged number of quantum signals and key generation rate is analyzed in our simulation, which offers a useful reference for experiment.     

Multi-physics analysis of the RFQ for Injector Scheme II of C-ADS driver linac

A 162.5 MHz, 2.1 MeV radio frequency quadruples （RFQ） structure is being designed for the Injector Scheme Ⅱ of the China Accelerator Driven Sub-critical System （C-ADS） linac. The RFQ will operate in continuous wave （CW） mode as required. For the CW normal conducting machine, the heat management will be one of the most important issues, since the temperature fluctuation may cause cavity deformation and lead to the resonant frequency shift. Therefore a detailed multi-physics analysis is necessary to ensure that the cavity can stably work at the required power level. The multi-physics analysis process includes RF electromagnetic analysis, thermal analysis, mechanical analysis, and this process will be iterated for several cycles until a satisfactory solution can be found. As one of the widely accepted measures, the cooling water system is used for frequency fine tunning, so the tunning capability of the cooling water system is also studied under different conditions. The results indicate that with the cooling water system, both the temperature rise and the frequency shift can be controlled at an acceptable level.     

Critical Behaviors in a Stochastic Local Limited One-Dimensional Rice-Pile Model

A stochastic local limited one-dimensional rice-pile model is numerically investigated. The distributions for avalanche sizes have a clear power-law behavior and it displays a simple finite size scaling. We obtain the avalanche exponents Ts= 1.54±0.10,βs = 2.17±0.10 and TT = 1.80±0.10, βT =1.46 ± 0.10. This self-organized critical model belongs to the same universality class with the Oslo rice-pile model studied by K. Christensen et al. [Phys. Rev. Lett. 77 （1996） 107], a rice-pile model studied by L.A.N. Amaral et al. [Phys. Rev. E 54 （1996） 4512], and a simple deterministic self-organized critical model studied by M.S. Vieira [Phys. Rev. E 61 （2000） 6056].     

Strategies for h-Adaptive Refinement for a Finite Element Treatment of Harmonic Oscillator Schrodinger Eigenproblem

A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.     

Design on a highly birefringent and nonlinear photonic crystal fiber in the C waveband

In this paper, a novel photonic crystal fiber （PCF） with high birefringence and nonlinearity is designed. The charac- teristics of birefringence, dispersion and nonlinearity are studied by using the full-vector finite element method （FVFEM）. The numerical results show that the phase birefringence and nonlinear coefficient of PCF can be up to 4.51× 10-3 and 32.8972 w-l.km-1 at 1.55 μm, respectively. The proposed PCF could be found to have important applications in the polarization-dependent nonlinear optics such as the pulse compress and reshaping in the C waveband.     

A Two-Dimensional Brans-Dicke Star Model with Exotic Matter and Dark Energy

A two-dimensional Brans-Dicke star model with exotic matter and dark energy is studied in this paper, the field equation and balance equation are derived at finite temperature, the analytic solutions of these equations can be used to calculate the mass of star. In addition, we find that star＇s mass has a minimum when matter state parameter γ→0.     

Dynamic investigation of the finite dissolution of silicon particles in aluminum melt with a lower dissolution limit

The finite dissolution model of silicon particles in the aluminum melt is built and calculated by the finite difference method, and the lower dissolution limit of silicon particles in the aluminum melt is proposed and verified by experiments, which could be the origin of microinhomogeneity in aluminum-silicon melts. When the effects of curvature and interface reaction on dissolution are not considered; the dissolution rate first decreases and later increases with time. When the effects of curvature and interface reaction on dissolution are considered, the dissolution rate first decreases and later increases when the interface reaction coefficient （k） is larger than 10 1, and the dissolution rate first decreases and later tends to be constant when k is smaller than 10-3. The dissolution is controlled by both diffusion and interface reaction when k is larger than 10-3, while the dissolution is controlled only by the interface reaction when k is smaller than 10-4.     

1+1维和2+1维空间上定向聚合问题的数值研究

对1+1和2+1维空间上定向聚合问题的数值模拟结果显示,任意有限温度下的横向涨落和自由能涨落在聚合尺度t较大时都将趋于零温度时强耦合下的结果:Δx∝t^ν和ΔF∝t^ω(d=1+1时,ν=2/3,ω=1/3;d=2+1时,ν≈0.6,ω≈0.2).有限温度下,由于1+1维和2+1维空间上的比热C(T,t)∝t和1+1维空间上的熵涨落ΔS∝t^1/2,1+1维空间上的系综能量涨落和内能涨落以及2+1维空间上的系综能量涨落均趋于t^1/2而远强于自由能涨落.在2+1维空间上,定向聚合问题有发生相变的迹象:当熵涨落达到其最大值时,单位聚合尺度的熵涨落和内能涨落在聚合尺度t→∞时,可能会由低温下趋于有限值(零温度除外)转变为高温下趋于零 关键词： 定向聚合 表面生长现象 Kardar-Parisi-Zhang方程     

Mechanical properties an undercut evaluated resonance test and of silicon nanobeams with by combining the dynamic finite element analysis

Mechanical properties of silicon nanobeams are of prime importance in nanoelectromechanical system applications. A numerical experimental method of determining resonant frequencies and Young＇s modulus of nanobeams by combining finite element analysis and frequency response tests based on an electrostatic excitation and visual detection by using a laser Doppler vibrometer is presented in this paper. Silicon nanobeam test structures are fabricated from silicon-oninsulator wafers by using a standard lithography and anisotropic wet etching release process, which inevitably generates the undercut of the nanobeam clamping. In conjunction with three-dimensional finite element numerical simulations incorporating the geometric undercut, dynamic resonance tests reveal that the undercut significantly reduces resonant frequencies of nanobeams due to the fact that it effectively increases the nanobeam length by a correct value △L, which is a key parameter that is correlated with deviations in the resonant frequencies predicted from the ideal Euler-Bernoulli beam theory and experimentally measured data. By using a least-square fit expression including △L, we finally extract Young＇s modulus from the measured resonance frequency versus effective length dependency and find that Young＇s modulus of a silicon nanobeam with 200-nm thickness is close to that of bulk silicon. This result supports that the finite size effect due to the surface effect does not play a role in the mechanical elastic behaviour of silicon nanobeams with thickness larger than 200 nm.     

Finite size specimens with cracks of icosahedral AI-Pd-Mn quasicrystals

Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.     

A new finite difference scheme for a dissipative cubic nonlinear Schr6dinger equation

This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.