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通过正则变换,构造出广义非线性Schr(o)dinger方程的多辛方程组.对此多辛方程组,导出了一个新的模方守恒多辛格式.数值实验结果表明,多辛格式具有长时间的数值行为,且在保持模方守恒律方面优于蛙跳格式和辛欧拉中点格式. 相似文献
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采用在点正则变换下形状不变势的映射方法,给出了将Poschl-Teller Ⅰ势映射至Poschl-Teller Ⅱ势的点正则变换,并从Poschl-TellerI势的束缚态能级和波函数求得了Poschl-Teller Ⅱ势的束缚态能级和波函数. 相似文献
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采用在点正则变换下形状不变势的映射方法,给出了将Poschl-Teller Ⅰ势映射至Poschl-Teller Ⅱ势的点正则变换,并从Poschl-TellerI势的束缚态能级和波函数求得了Poschl-Teller Ⅱ势的束缚态能级和波函数. 相似文献
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本文给出了二维Heisenberg反铁磁系统中的正则变换.在此变换下发现二维Heisenberg反铁磁模型在连续极限下是具有拓扑项的O(3)非线性σ模型.由于在选取正则变量时有很大的不确定性,因此还不能判定此系统是否确有拓扑项存在.最后对正则变换的物理意义进行了研究,发现它体现了系统自旋的集体激发,表明存在着一种自旋波. 相似文献
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用相空间中向量场的概念给出了正则变换的充要条件的一种证明,同时证明了泊松括号于正则变换下的不变性,指出了一般教材中的一些不明确之处。 相似文献
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利用无线电全息方法, 如正则变换方法或全谱反演方法, 可以有效地解决大气多路径条件下GPS掩星信号的反演问题. 本文采用正则变换方法反演掩星资料, 模拟仿真反演结果显示正则变换方法可以准确地反演包含大气多路径效应的信号. 在模拟信号的相位中加入不同程度的高斯相位噪声后, 正则变换方法的反演结果会受到不同程度的影响. 用正则变换方法对2007年第71天至73天共约4500个COSMIC数据进行处理. 将其折射率反演结果和atmPrf资料 (利用全谱反演方法计算得到) 一起, 与对应的ECMWF 分析场资料进行统计比较, 结果表明: 在5 km以下, 正则变换方法计算的折射率的相对误差的平均值普遍大于atmPrf资料. 其原因可能为: 正则变换方法将信号从LEO轨迹后传播至辅助屏, 造成孔径缩小, 精度下降. 同时也讨论了信号截断对低对流层中反演精度和掩星个数的影响.
关键词:
无线电掩星
大气多路径
多相位屏技术
正则变换方法 相似文献
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给出构造Hamilton系统的准正则变换的方法,首先将Hamilton系统变换成Birkhoff系统,然后将Birkhoff系统作规范变换并实现Hamilton化. 指出对一个Hamilton系统存在多种准正则变换. 举例说明所得结果的应用.
关键词:
Hamilton系统
准正则变换
Birkhoff系统
规范变换 相似文献
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采用在点正则变换下形状不变势的映射方法 ,给出了将P schl TellerⅠ势映射至P schl TellerⅡ势的点正则变换 ,并从P schl TellerI势的束缚态能级和波函数求得了P schl TellerⅡ势的束缚态能级和波函数 相似文献
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将电磁波导的控制方程导向了Hamilton体系、辛几何的形式.以电磁场的横向分量组成对偶向量并采用分离变量法,可以得到Hamilton算子矩阵的辛本征值问题.共轭辛正交归一关系、辛本征解展开定理等均可在此应用.对于复杂横截面和填充非均匀材料的电磁波导,提出对偶棱边元,对截面半解析离散后即可进行数值求解.对偶棱边元克服了结点基有限元求解电磁场问题的困难,与常规棱边元相比在某些方面具有一定的优势.
关键词:
电磁波导
Hamilton体系
对偶变量
棱边元 相似文献
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Morrison [25] has observed that the Maxwell-Vlasov and Poisson-Vlasov equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisson bracket. We derive another Poisson structure for these equations by using general methods of symplectic geometry. The main ingredients in our construction are the symplectic structure on the co-adjoint orbits for the group of canonical transformations, and the symplectic structure for the phase space of the electromagnetic field regarded as a gauge theory. Our Poisson bracket satisfies the Jacobi identity, whereas Morrison's does not [37]. Our construction also shows where canonical variables can be found and can be applied to the Yang-Mills-Vlasov equations and to electromagnetic fluid dynamics. 相似文献
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In the previous papers I and II,we have studied the difference discrete variational principle and the Euler-Lagrange cohomology in the framework of multi-parameter differential approach.We have gotten the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the lagrangian and Hamiltonian formalisms.In this paper,we apply the difference discrete variational principle and Euler-Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms.We will show that either Hamiltonian schemes of Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler-Lagrange cohomological conditions are satisfied. 相似文献
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In the previous papers I and H, we have studied the difference discrete variational principle and the EulerLagrange cohomology in the framework of multi-parameter differential approach. W5 have gotten the difference discreteEulcr-Lagrangc equations and canonical ones for the difference discrete versions of classical mechanics and tield theoryas well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessaryand sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the Lagrangianand Hamiltonian formalisms. In this paper, we apply the difference discrete variational principle and Euler-Lagrangecohomological approach directly to the symplectic and multisymplectic algorithms. We will show that either Hamiltonianschemes or Lagrangian ones in both the symplectic and multisymplectic algorithms arc variational integrators and theirdifference discrete symplectic structure-preserving properties can always be established not only in the solution spacebut also in the function space if and only if the related closed Euler Lagrange cohomological conditions are satisfied. 相似文献
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Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics 总被引:1,自引:0,他引:1
The evolutionary dynamics first conceived by Darwin and Wallace, referring to as Darwinian dynamics in the present paper, has been found to be universally valid in biology. The statistical mechanics and thermodynamics, while enormous successful in physics, have been in an awkward situation of wanting a consistent dynamical understanding. Here we present from a formal point of view an exploration of the connection between thermodynamics and Darwinian dynamics and a few related topics. We first show that the stochasticity in Darwinian dynamics implies the existence temperature, hence the canonical distribution of Boltzmann-Gibbs type. In term of relative entropy the Second Law of thermodynamics is dynamically demonstrated without detailed balance condition, and is valid regardless of size of the system. In particular, the dynamical component responsible for breaking detailed balance condition does not contribute to the change of the relative entropy. Two types of stochastic dynamical equalities of current interest are explicitly discussed in the present approach: One is based on Feynman-Kac formula and another is a generalization of Einstein relation. Both are directly accessible to experimental tests. Our demonstration indicates that Darwinian dynamics represents logically a simple and straightforward starting point for statistical mechanics and thermodynamics and is complementary to and consistent with conservative dynamics that dominates the physical sciences. Present exploration suggests the existence of a unified stochastic dynamical framework both near and far from equilibrium. 相似文献
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Debendranath Sahoo 《Pramana》1978,10(3):273-282
A Bose type of classical Hamilton algebra, i.e., the algebra of the canonical formalism of classical mechanics, is represented
on a linear space of functions of phase space variables. The symplectic metric of the phase space and possible algorithms
of classical mechanics (which include the standard one) are derived. It is shown that to each of the classical algorithms
there is a corresponding one in the phase space formulation of quantum mechanics. 相似文献
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The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group. 相似文献