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研究一类动力学方程的Mei对称性的定义和判据,由Mei对称性通过Noether对称性可找到Noether守恒量.由Mei对称性通过Lie对称性可找到Hojman守恒量.同时,也可找到一类新型守恒量. 相似文献
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Mei symmetry and conservation laws of discrete nonholonomic dynamical systems with regular and irregular lattices 下载免费PDF全文
In this paper,Noether symmetry and Mei symmetry of discrete nonholonomic dynamical systems with regular and the irregular lattices are investigated.Firstly,the equations of motion of discrete nonholonomic systems are introduced for regular and irregular lattices.Secondly,for cases of the two lattices,based on the invariance of the Hamiltomian functional under the infinitesimal transformation of time and generalized coordinates,we present the quasi-extremal equation,the discrete analogues of Noether identity,Noether theorems,and the Noether conservation laws of the systems.Thirdly,in cases of the two lattices,we study the Mei symmetry in which we give the discrete analogues of the criterion,the theorem,and the conservative laws of Mei symmetry for the systems.Finally,an example is discussed for the application of the results. 相似文献
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研究Hamilton系统的形式不变性即Mei对称性,给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系,寻求系统的守恒量.给出一个例子说明本文结果的应用.
关键词:
Hamilton系统
Mei对称性
Noether对称性
Lie对称性
守恒量 相似文献
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We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon–Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered. 相似文献
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The Mei symmetry of Tzénoff equations under the infinitesimal transformations of groups is studied in this paper. The definition and the criterion equations of the symmetry are given. If the symmetry is a Noether symmetry, then the Noether conserved quantity of the Tzénoff equations can be obtained by the Mei symmetry. 相似文献
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We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced. 相似文献
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This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result. 相似文献
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We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced. 相似文献
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XIA Li-Li LI Yuan-Cheng WANG Jing HOU Qi-Bao 《理论物理通讯》2006,46(3):415-418
This paper concentrates on studying the symmetries and a new type of conserved quantities called Mei conserved quantity. The criterions of the Mei symmetry, the Noether symmetry and the Lie symmetry are given. The conditions and the forms of the Mei conserved quantities deduced from these three symmetries are obtained. An example is given to illustrate the application of the result. 相似文献
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A consistent tanh expansion (CTE) method is used to study the modified Boussinesq equation. It is proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by the Painlevé analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependent variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initial value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among solitons and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wave interaction behaviors are studied both in analytical and graphical ways. 相似文献
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In this paper, the Lie symmetry algebra of the coupled
Kadomtsev--Petviashvili (cKP) equation is obtained by the classical Lie group method and
this algebra is shown to have
a Kac--Moody--Virasoro loop algebra structure. Then the general symmetry groups of the cKP
equation is also obtained by the symmetry group direct method which is proposed by Lou et al。 From the
general symmetry groups, the Lie symmetry group can be recovered and a group
of discrete transformations can be derived simultaneously. Lastly,
from a known simple solution of the cKP equation, we can easily obtain
two new solutions by the general symmetry groups. 相似文献
14.
Jasper van Wezel 《Physica B: Condensed Matter》2008,403(18):3206-3210
We show how a local pairing model for superconductivity can be used to describe the symmetry breaking mechanism in exact analogy to the cases of quantum crystals and antiferromagnets. We find that there are low energy states associated with the symmetry breaking process which are not influenced by the Anderson-Higgs mechanism. The presence of these ‘thin spectrum’ states in qubits based on superconducting material leads to a maximum time for which such qubits can remain quantum coherent. We also show how the charging energy of superconducting quantum dots may give the thin spectrum states a finite energy gap, impeding the spontaneous breaking of phase symmetry. 相似文献
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In quantum theory, symmetries more general than groups are possible. We give a general definition of a quantum symmetry, such that symmetry operations act on the Hilbert space
of physical states and notions of unitarity, invariance and covariance are defined. Within this frame, weak quasi quantum groups are described as a natural generalization of group algebras. Consistency with locality distinguishes them from more general quantum symmetries. To find the new kinds of symmetry one should investigate low dimensional quantum systems such as two-dimensional layers. 相似文献
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Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated.Firstly,the Noether symmetry of a discrete mechanico-electrical system is reviewed,and the motion equations and energy equations are derived.Secondly,the definition of Noether-Mei symmetry for the system is presented,and the criterion is derived.Thirdly,conserved quantities induced by Noether-Mei symmetry with their existence conditions are obtained.Finally,an example is discussed to illustrate the results. 相似文献
17.
Noether symmetry and Lie symmetry of discrete holonomic systems with dependent coordinates 下载免费PDF全文
The Noether symmetry, the Lie symmetry and the conserved quantity of discrete holonomic systems with dependent coordinates are investigated in this paper. The Noether symmetry provides a discrete Noether identity and a conserved quantity of the system. The invariance of discrete motion equations under infinitesimal transformation groups is defined as the Lie symmetry, and the condition of obtaining the Noether conserved quantity from the Lie symmetry is also presented. An example is discussed to show the applications of the results. 相似文献
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Based on some known facts of integrable models, this paper proposes a new (2+1)-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied 相似文献
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The polarization effect on the spin symmetry for anti-Lambda spectrum in 16 O+Λ system has been studied in relativistic mean-field theory.The PK1 effective interaction is used for nucleon-meson couplings and G-parity symmetry with a reduction factor ξ = 0.3 is adopted for anti-Lambda-meson couplings.The energy differences between spin doublets in the anti-Lambda spectrum are around 0.10-0.73 MeV for p Λ state.The dominant components of the Dirac spinor for the anti-Lambda spin doublets are found to be near identical.It indicates that the spin symmetry is still well-conserved against the polarization effect from the valence antiLambda hyperon,which leads to a highly compressed cold nucleus with the central density up to 2 - 3 times of saturated density. 相似文献