Impact of symmetrized and Burt—Foreman Hamiltonians on spurious solutions and energy levels of InAs/GaAs quantum dots

<正>We present a systematic investigation of calculating quantum dots(QDs) energy levels using the finite element method in the frame of the eight-band k·p method.Numerical results including piezoelectricity,electron and hole levels,as well as wave functions are achieved.In the calculation of energy levels,we do observe spurious solutions(SSs) no matter Burt-Foreman or symmetrized Hamiltonians are used.Different theories are used to analyse the SSs,we find that the ellipticity theory can give a better explanation for the origin of SSs and symmetrized Hamiltonian is easier to lead to SSs.The energy levels simulated with the two Hamiltonians are compared to each other after eliminating SSs,different Hamiltonians cause a larger difference on electron energy levels than that on hole energy levels and this difference decreases with the increase of QD size.     

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.     

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.     

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].     

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.     

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 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.     

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.     

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.     

Finite Size Effect in Path Integral Monte Carlo Simulations of ^4He Systems

Path integral Monte Carlo （PIMC） simulations are a powerful computational method to study interacting quantum systems at finite temperatures. In this work, PIMC has been applied to study the finite size effect of the simulated systems of ^4He. We determine the energy as a function of temperature at saturated-vapor-pressure （SVP） conditions in the temperature range of T ∈ [1.0 K,4.0 K], and the equation of state （EOS） in the grmmd state For systems consisted of 32, 64 and 128 ^4He atoms, respectively, We find that the energy at SVP is influenced significantly by the size of the simulated system in the temperature range of T ∈ [2.1 K, 3.0 K] and the larger the system is, the better results are obtained in comparison with the experimental values; while the EOS appeared to be unrelated to it.     

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.     

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.     

Casimir Force at a Finite Cut-Off

We calculate the Casimir force at a finite cut-off Λ 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 LΛ → ∞. There is a correction in the order of (LΛ)^-2, when LΛ is finite and large. This correction becomes remarkable when L is comparable with the microscopic length scale Λ^-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.     

△-Resonances in Ground State Properties of ^40 20Ca Spherical Cold Finite Nucleus at Equilibrium and under Compression

The ground state properties of the spherical nucleus ^40Ca have been investigated by using constrained spherical Hartree Fock （CSHF） approximation at equilibrium and under high radial compression in a six major shells. The effective baryon-baryon interaction that includes the △（1236） resonance freedom degrees to calculate nuclear properties is used. The nucleon-nucleon （N-N） interaction is based on Reid soft core （RSC） potential. The results of calculations show that much of increase in the nuclear energy generated under compression is used to create the massive △ particles. The number of △ ＇s can be increased to about 2.1% of constituents of nucleus when nuclear density reaches about 1.34 times of normal density. The single particle energy levels are calculated and their behavior under compression is also examined. △ good agreement has been found between current calculations and phenomenological shell model for low lying single-particle spectra. The gap between shells is very clear and L-S coupling become stronger as increasing the static load on the nucleus. The results show a considerable reduction in compressibility when freedom degrees of △＇s are taken into account. It has been found that the total nuclear radial density becomes denser in the interior and less dense in the exterior region of nucleus. The surface of nucleus becomes more and more responsive to compression than outer region.     

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.     

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.     

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.     

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.     

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.     

Criticality in Two-Variable Earthquake Model on a Random Graph

A two-variable earthquake model on a quenched random graph is established here. It can be seen as a generalization of the OFC models. We numerically study the critical behavior of the model when the system is nonconservative： the result indicates that the model exhibits self-organized criticality deep within the nonconservative regime. The probability distribution for avalanche size obeys finite size scaling. We compare our mode/with the mode/ introduced by Stefano Lise and Maya Paczuski [Phys. Rev. Lett. 88 （2002） 228301], it is proved that they are not in the same universality class.