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1.
An anti-symmetric loop algebra \overline{A}_2 is constructed. It follows that an integrable system is obtained by use of Tu's scheme. The eminent feature of this integrable system is that it is reduced to a generalized Schr?dinger equation, the well-known heat-conduction equation and a Gerdjkov-Ivanov (GI) equation. Therefore, we call it a generalized SHGI hierarchy. Next, a new high-dimensional subalgebra \tilde{G} of the loop algebra ?_2 is constructed. As its application, a new expanding integrable system with six potential functions is engendered. 相似文献
2.
Using the technique of integration within an ordered product of operators, we construct a new common eigenvector set of the complex scalar fields φ(x) and φ?(x), which is a set of particle-antiparticle correlated states. On the basis of the new eigenstates we develop the path integral formuation. The new eigenvectors' properties are investigated, they are qualified to be a new representation. 相似文献
3.
Determination of the stellar reaction rate for 12C(α,γ)16O: using a new expression with the reaction mechanism 下载免费PDF全文
The astrophysical reaction rate of 12C(α, γ)16O plays a key role in massive star evolution. However, this reaction rate and its uncertainties have not been well determined yet, especially at T9=0.2. The existing results even disagree with each other to a certain extent. In this paper, the E1, E2 and total (E1+E2) 12C(α, γ)16O reaction rates are calculated in the temperature range from T9=0.3 to 2 according to all the available cross section data. A new analytic expression of the 12 C(α, γ)16 O reaction rate is brought forward based on the reaction mechanism. In this expression, each part embodies the underlying physics of the reaction. Unlike previous works, some physical parameters are chosen from experimental results directly, instead of all the parameters obtained from fitting. These parameters in the new expression, with their 3σ fit errors, are obtained from fit to our calculated reaction rate from T9=0.3 to 2. Using the fit results, the analytic expression of 12C(α, γ)16O reaction rate is extrapolated down to T9=0.05 based on the underlying physics. The 12C(α, γ)16 O reaction rate at T9=0.2 is (8.78 ± 1.52) × 1015 cm3s-1mol-1. Some comparisons and discussions about our new 12 C(α, γ)16 O reaction rate are presented, and the contributions of the reaction rate correspond to the different part of reaction mechanism are given. The agreements of the reaction rate below T9=2 between our results and previous works indicate that our results are reliable, and they could be included in the astrophysical reaction rate network. Furthermore, we believe our method to investigate the 12C(α, γ)16O reaction rate is reasonable, and this method can also be employed to study the reaction rate of other astrophysical reactions. Finally, a new constraint of the supernovae production factor of some isotopes are illustrated according to our 12C(α, γ)16O reaction rates. 相似文献
4.
A new global potential energy surface of the ground state of SiH2+ (X2A1) system and dynamics calculations of the Si+ + H2 (v0 = 2, j0 = 0) → SiH+ + H reaction 下载免费PDF全文
Yong Zhang 《中国物理 B》2022,31(11):113101-113101
A global potential energy surface (PES) of the ground state of SiH$_{2}^{+}$ system is built by using neural network method based on 18223 ab initio points. The topographic properties of PES are presented and compared with previous theoretical and experimental studies. The results indicate that the spectroscopic parameters obtained from the new PES are in good agreement with the experimental data. In order to further verify the validity of the new PES, a test dynamics calculation of the Si$^{+} +$ H$_{2}$ ($v_0 = 2, j_{0} = 0$) $\to $ H $+$ SiH$^{+}$ reaction has been carried out by using the time-dependent wave packet method. The integral cross sections and rate constants are computed for the title reaction. The reasonable dynamical behavior indicates that the newly constructed PES is suitable for relevant dynamics investigations. 相似文献
5.
Coherent interaction and action-counteraction theory in small polaron systems,and ground state properties 下载免费PDF全文
Zhi-Hua Luo 《中国物理 B》2022,31(11):117104-117104
Based on the coherent interaction and action-counteraction principles, we investigate the ground state properties for small polaron systems, the coherent-squeezed fluctuation correction, and the anomalous lattice quantum fluctuation, with the new variational generator containing correlated squeezed-coherent coupling and quantum entanglement. Noting that $-2t $ is the T.B.A. energy, for the coherent interaction effect, we find the ground-state energy $E_0$ to be $-2.428t$, in which the coherent squeezed fluctuation correction $-A_0 t$ is $-0.463t $ (where $ t $ is the hopping integral, $\omega $ is the phonon frequency), with the electron-one-phonon coupling constant $g=$1 and the electron-two-phonon coupling constant $g_{1}=-0.1$. However, as a result of the action-counteraction effect, $\tilde{{E}}_{0} $ is $-2.788t$, but $-\tilde{{A}}_{0} t$ is $-0.735t$. As to the polaron binding energy $(E_{\rm P} )$, for the coherent interaction effect, $E_{\rm P} $ is $-1.38\omega $, but for the action-counteraction effect, $\tilde{{E}}_{\rm P}$ is $-1.88\omega $. In particular, the electron-two-phonon interaction noticeably enlarges the coherent interaction and the coherent squeezed quantum fluctuation correction. By intervening with the quantum entanglement, the evolutions of the squeezed coherent state and the lattice quantum fluctuation begin to take control. At that time, we encounter a new quantum phase coherence phenomenon — the collapse and revival of inversion repeatedly for the coherent state in the entangled evolution. 相似文献
6.
An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system 下载免费PDF全文
A subalgebra of loop algebra ?_2 is established. Therefore, a new isospectral problem is designed. By making use of Tu's scheme, a new integrable system is obtained, which possesses bi-Hamiltonian structure. As its reductions, a formalism similar to the well-known Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and a generalized standard form of the Schr?dinger equation are presented. In addition, in order for a kind of expanding integrable system to be obtained, a proper algebraic transformation is supplied to change loop algebra ?_2 into loop algebra ?_1. Furthermore, a high-dimensional loop algebra is constructed, which is different from any previous one. An integrable coupling of the system obtained is given. Finally, the Hamiltonian form of a binary symmetric constrained flow of the system obtained is presented. 相似文献
7.
采用双层线性耦合Lengyel-Epstein模型,在二维空间对简单正四边和超点阵四边形进行了数值分析.结果表明:当两子系统波数比N1时,随耦合强度的增大,基模的波矢空间共振形式发生改变,系统由简单六边形自发演化为结构复杂的新型斑图,除已报道的超六边形外,还获得了简单正四边和多种超点阵四边形,包括大小点、点线、白眼和环状超四边等斑图.当耦合系数α和β在一定范围内同步增大时,两子系统形成相同波长的Ⅰ型简单正四边;当α和β不同步增大时,由于两图灵模在短波子系统形成共振,系统斑图经相变发生Ⅰ型正四边→Ⅱ型正四边→超点阵四边形的转变;当系统失去耦合作用时,短波子系统波长为λ的Ⅰ型正四边斑图迅速失稳并形成波长为λ/N的Ⅰ型正四边,随模拟时间的延长,两子系统中不同波长的正四边均会经相变发生Ⅰ型正四边→Ⅱ型正四边→六边形的转变. 相似文献
8.
This paper proposes a new Zernike modal gray map
reconstruction algorithm used in the nematic liquid crystal adaptive
optics system. Firstly, the new modal algorithm is described. Secondly,
a single loop correction experiment was conducted, and it showed
that the modal method has a higher precision in gray map
reconstruction than the widely used slope method. Finally, the
contrast close-loop correction experiment was conducted to correct
static aberration in the laboratory. The experimental results showed
that the average peak to valley (PV) and root mean square (RMS) of
the wavefront corrected by mode method were reduced from
2.501\lambda (\lambda =633~nm) and 0.610\lambda to
0.0334\lambda and 0.00845\lambda , respectively. The corrected
PV and RMS were much smaller than those of 0.173\lambda and
0.048\lambda by slope method. The Strehl ratio and modulation
transfer function of the system corrected by mode method were much
closer to diffraction limit than with slope method. These results
indicate that the mode method can take good advantage of the large
number of pixels of the liquid crystal corrector to realize high
correction precision. 相似文献
9.
A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics 下载免费PDF全文
In this paper we first present a CG-type method for inverse
eigenvalue problem of constructing real and symmetric matrices $M$,
$D$ and $K$ for the quadratic pencil $Q(\lambda)=\lambda^2M+\lambda
D+K$, so that $Q(\lambda)$ has a prescribed subset of eigenvalues
and eigenvectors. This method can determine the solvability of the
inverse eigenvalue problem automatically. We then consider the least
squares model for updating a quadratic pencil $Q(\lambda)$. More precisely,
we update the model coefficient matrices $M$, $C$ and $K$ so
that (i) the updated model reproduces the measured data, (ii) the
symmetry of the original model is preserved, and (iii)
the difference between the analytical triplet $(M, D, K)$ and the
updated triplet $(M_{\text{new}}, D_{\text{new}},
K_{\text{new}})$ is minimized. In this paper a
computationally efficient method is provided for such model updating
and numerical examples are given to illustrate the effectiveness of
the proposed method. 相似文献
10.
It is noted that in the new Particle Data Group(PDG) version the rare decays of the Λ_b baryon have been revised with more accuracy. The new results show that most of the existing theoretical results on the process Λ_b→Λ_γ Lgbare larger than those of experiments. With the improved higher-order light-cone distribution amplitudes of the Λ baryon, we reanalyze the process in the framework of light-cone quantum chromodynamics sum rules and the branching ratio is estimated to be Br (Λ_b→Λ_γ)=(7.38_(-0.39)~(+0.40))×10~(16), which is consistent with the new experimental result. Furthermore, another process Λ_b→Λl~+l~- is also analyzed in the same frame. The final branching ratio is calculated to be Br (Λ_b→Λl~+l~-)=1.20×10~(-6), which is in good accordance with the data from the PDG and other theoretical predictions. 相似文献
11.
Finite-dimensional even and odd nonlinear pair coherent states and their some nonclassical properties 下载免费PDF全文
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states (EONLPCSs), which can be realized via operating the superposed evolution operators D±(τ) on the state |q, 0), is constructed, then their orthonormalized property, completeness relations and some nonclassical properties are discussed. It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations. Moreover, the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q, η and ξ. 相似文献
12.
By making use of the φ-mapping topological current theory, this paper shows that the Gauss-Bonnet-Chern density (the Euler-Poincaré characteristic χ(M) density) can be expressed in terms of a smooth vector field φ and take the form of δ(φ), which means that only the zeros of φ contribute to χ(M). This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of -branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi -branes. 相似文献
13.
Synchronizability of complex oscillators networks has attracted much
research interest in recent years. In contrast, in this paper we
investigate numerically the synchronization speed, rather than the
synchronizability or synchronization stability, of identical
oscillators on complex networks with communities. A new weighted
community network model is employed here, in which the community
strength could be tunable by one parameter δ. The results
showed that the synchronization speed of identical oscillators on
community networks could reach a maximal value when δ is
around 0.1. We argue that this is induced by the competition
between the community partition and the scale-free property of the
networks. Moreover, we have given the corresponding analysis through
the second least eigenvalue λ2 of the Laplacian matrix of
the network which supports the previous result that the
synchronization speed is determined by the value of λ2. 相似文献
14.
Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems 下载免费PDF全文
Chao Yue Aiguo Xiao & Hongliang Liu 《advances in applied mathematics and mechanics.》2015,7(4):472-495
In this paper, we are devoted to nonlinear stability and B-convergence of
additive Runge-Kutta (ARK) methods for nonlinear stiff problems with multiple stiffness.
The concept of ($θ$,$\bar{p}$,$\bar{q}$)-algebraic stability of ARK methods for a class of stiff
problems $K_{σ,τ}$ is introduced, and it is proven that this stability implies some contractive
properties of the ARK methods. Some results on optimal B-convergence of ARK
methods for $K_{σ,0}$ are given. These new results extend the existing ones of RK methods
and ARK methods in the references. Numerical examples test the correctness of our
theoretical analysis. 相似文献
15.
Magdy A. Ezzat A. S. Sabbah A. A. El-Bary & S. M. Ezzat 《advances in applied mathematics and mechanics.》2015,7(4):528-548
A new mathematical model of magnetohydrodynamic (MHD) theory has
been constructed in the context of a new consideration of heat conduction with a time-fractional
derivative of order 0<$α$≤1 and a time-fractional integral of order 0<$γ$≤2.
This model is applied to one-dimensional problems for a thermoelectric viscoelastic
fluid flow in the absence or presence of heat sources. Laplace transforms and state-space
techniques [1] will be used to obtain the general solution for any set of boundary
conditions. According to the numerical results and its graphs, conclusion about the
new theory has been constructed. Some comparisons have been shown in figures to
estimate the effects of the fractional order parameters on all the studied fields. 相似文献
16.
We present a new global fit to precision electroweak data, including new low- and high-energy data and analyzing the radiative corrections arising from the minimal symmetry breaking sectors of the Standard Model (SM) and its supersymmetric extension (MSSM). It is shown that present data favor a Higgs mass of ${cal O}(M_Z)$: $$M_{H}=76 {+ 152 ?op -50}{? GeV}.$$ We confront our analysis with (meta) stability and perturbative bounds on the SM Higgs mass, and the theoretical upper bound on the MSSM Higgs mass. Present data do not discriminate significantly between the SM and MSSM Higgs mass ranges. We comment in passing on the sensitivity of the Higgs mass determination to the values of $←pha (M_Z)$ and ${←pha_s} (M_Z)$. 相似文献
17.
我们研究一个耦合2谐振子系统的本征态问题。我们构造了由算子(x1+p2)和(x2+p1)的共同本征态组成的新纠缠态表象︱γ>。在︱γ>表象得到了系统哈密顿的本征值和本征态。同样的问题用二次量子化表象进行了研究。我们发现在Fock空间,二次量子化表象可以被用来推得本征态的正规积表示。特别是发现了系统基态为广义2模压缩态 相似文献
18.
We use a new updated algorithm scheme to investigate the critical behaviour of the two-dimensional ferromagnetic Ising model on a triangular lattice with the nearest neighbour interactions. The transition is examined by generating accurate data for lattices with L= 8, 10, 12, 15, 20, 25, 30, 40 and 50. The updated spin algorithm we employ has the advantages of both a Metropolis algorithm and a single-update method. Our study indicates that the transition is continuous at Tc= 3.6403({2}). A convincing finite-size scaling analysis of the model yields υ=0.9995(21), β /
υ = 0.12400({17}), γ / υ = 1.75223(22), γ '/υ=1.7555(22), α/υ= 0.00077(420) (scaling) and α / υ = 0.0010(42) (hyperscaling). The present scheme yields more accurate estimates for all the critical exponents than the Monte Carlo method, and our estimates are shown to be in excellent agreement with their predicted values. 相似文献
19.
Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations 总被引:1,自引:0,他引:1 下载免费PDF全文
For a relativistic holonomic nonconservative system, by using the
Noether symmetry, a new non-Noether conserved quantity is given under
general infinitesimal transformations of groups. On the basis of the
theory of invariance of differential equations of motion under
general infinitesimal transformations, we construct the relativistic
Noether symmetry, Lie symmetry and the condition under which the
Noether symmetry is a Lie symmetry under general infinitesimal
transformations. By using the Noether symmetry, a new relativistic
non-Noether conserved quantity is given which only depends on the
variables $t$, $q_s $ and $\dot {q}_s $. An example is given to
illustrate the application of the results. 相似文献
20.
International Journal of Theoretical Physics - A new kind of symmetry behaviour introduced as partial $\mathcal {P}\mathcal {T}$ -symmetry(henceforth $\partial _{\mathcal {P}\mathcal {T}}$ ) is... 相似文献