Classical geometry of bosonic string dynamics

We develop a treatment of bosonic strings on a general curved background in which the volume element and the coordinates of the worldsheet are related in a similar way as canonically conjugate quantities in mechanics. The resultant formalism is a particular variant of the multi-phase-space approach to classical field theory put forward by Kijowski, Tulczyjew, and others. We study conservation laws within this framework and find that all conserved quantities are related to point symmetries, i.e., isometries of the underlying spacetime. Thus, the symmetries of relativistic mechanics coming from Killing tensors have no analogue here. We furthermore deduce from the present scheme the covariant version of the usual phase space.     

Unified approach to the conservation laws and soliton solution for sine-gordon system

It is possible to generate an infinite number of conserved quantities and the most general soliton solution in an arbitrary background with the help of the Darboux-Backlund transformation and an expansion of the Lax eigenfunction in the eigenvalue parameter. Use is not made of the Riccati form of the Lax equation which is used in the usual derivation of the conserved quantities. It is shown that for zero seed solution one retrieves the usual one-soliton solution.     

Conservation law for multimoded nonlinear optical waveguide interactions and its physical interpretation

The swapping of power between the modes of cw waves in lossless nonlinear optical waveguides always admit two conserved quantities, the total power and one other, which is sometimes identified as a Hamiltonian. We show that a general formulation of this Hamiltonian is in fact the weak guidance limit for cw waves of a more general conservation law. We make the link between this more general conservation law and the conservation of "wave" momentum, where wave momentum is a combination of both real momentum and so-called pseudomomentum. This allows us to interpret the conserved Hamiltonian in physical terms.     

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems.Firstly,we give the definition of integrating factors for the differential equations of motion of a mechanical system.Next,the necessary conditions for the existemce of the conserved quantities are studied in detail.Then,we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system.Finally,an exampled is given to illustrate the application of the result.     

Manifestly-covariant canonical formalism of Poincaré gauge theories

We present a general framework for manifestly-covariant canonical formulation of Poincaré gauge theories. We construct a general class of action that is invariant under two kinds of BRS transformations—translation and internal Lorentz—and suitable for manifestly-covariant canonical quantization. This theory contains a great number of conserved quantities, which we investigate systematically. It is also pointed out that a canonical formulation of higher-derivative theories may be obtained as a limiting case in this framework.     

New non-Noether conserved quantities of mechanical system in phase space

This paper focuses on studying non-Noether conserved quantities of Lie symmetry and of form invariance for a mechanical system in phase space under the general infinitesimal transformation of groups. We obtain a new non-Noether conserved quantity of Lie symmetry of the system, and Hojman and Mei's results are of special cases of our conclusion. We find a condition under which the form invariance of the system will lead to a Lie symmetry, and, further, obtain a new non-Noether conserved quantity of form invariance of the system. An example is given finally to illustrate these results.     

二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法与对称性研究

将扩展Prelle-Singer法(扩展P-S法)用于求x=Ф1(x,y),y=Ф2(x,y)类型的二阶非线性耦合动力学系统的守恒量,得到了积分乘子满足的微分方程与守恒量的一般形式,并讨论所得守恒量的Noether对称性与Lie对称性.最后用扩展P-S法求得了四次非谐振子系统的两个守恒量,并讨论了系统的对称性.     

Quantum Toda systems and Lax pairs

We describe a general method for constructing a Lax pair representation of certain quantum mechanical systems that are integrable at the classical level. This is then used to find conserved quantities at the quantum level for the Toda systems.     

Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system.On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation,the determining equations,the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed.The criterions of Mei symmetries,weak Mei symmetries and strong Mei symmetries of the system are given.New types of conserved quantities,i.e.the Mei symmetrical conserved quantities,the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system,are obtained.Then,a deduction of the first-order nonholonomic system is discussed.Finally,two examples are given to illustrate the application of the method and then the results.     

含非线性微扰项的二阶动力学系统的一阶近似守恒量的一种新求法

从一阶近似守恒量的性质出发,把受微扰系统视为未受微扰系统与微扰项的迭加,提出一种分三步求得一阶近似守恒量的新方法:先选择合适的方法求得未受微扰系统的守恒量I0,再考虑微扰项对守恒量I0的影响,最后利用一阶近似守恒量的性质求得一阶近似守恒量.用该方法研究了一实际的受非线性微扰作用的两自由度动力学系统,得到4个稳定的一阶近似守恒量.用坐标变换法和微扰法得到系统一阶近似解的表达式,并讨论4种特殊情况下的一阶近似解.     

三自由度二阶非线性耦合动力学系统守恒量的扩展Prelle-Singer求法

用扩展Prelle-Singer法(扩展P-S法)求三自由度二阶非线性耦合动力学系统的守恒量,得到了6个积分乘子满足的确定方程、约束方程和守恒量的一般形式,并讨论了确定积分乘子的方法.最后,用扩展P-S法求得了三质点Tada晶格问题的两个守恒量.     

Role of conserved quantities in Fourier's law for diffusive mechanical systems

Energy transport can be influenced by the presence of other conserved quantities. We consider here diffusive systems where energy and the other conserved quantities evolve macroscopically on the same diffusive space–time scale. In these situations, the Fourier law depends also on the gradient of the other conserved quantities. The rotor chain is a classical example of such systems, where energy and angular momentum are conserved. We review here some recent mathematical results about the diffusive transport of energy and other conserved quantities, in particular for systems where the bulk Hamiltonian dynamics is perturbed by conservative stochastic terms. The presence of the stochastic dynamics allows us to define the transport coefficients (thermal conductivity) and in some cases to prove the local equilibrium and the linear response argument necessary to obtain the diffusive equations governing the macroscopic evolution of the conserved quantities. Temperature profiles and other conserved quantities profiles in the non-equilibrium stationary states can be then understood from the non-stationary diffusive behavior. We also review some results and open problems on the two step approach (by weak coupling or kinetic limits) to the heat equation, starting from mechanical models with only energy conserved.     

变质量非完整系统Tzénoff方程的Lie对称性与其导出的守恒量

航天器运行系统大都属于变质量力学系统,变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律.本文首先导出了变质量非完整力学系统的Tzénoff方程,然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量,给出了这种守恒量的函数表达式和导出这种守恒量的判据方程.该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.     

Einstein-Dirac theory on gauge-natural bundles

We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan) gravity coupled with Dirac fields gives rise to an unexpected indeterminacy in the concept of conserved quantities.     

变质量非完整系统Tzénoff方程的Lie 对称性与其导出的守恒量

航天器运行系统大都属于变质量力学系统, 变质量力学系统的对称性和守恒量隐含着航天系统更深刻的物理规律. 本文首先导出了变质量非完整力学系统的Tzénoff方程, 然后研究了变质量非完整力学系统Tzénoff方程的Lie对称性及其所导出的守恒量, 给出了这种守恒量的函数表达式和导出这种守恒量的判据方程. 该研究结果对进一步探究变质量系统所遵循的守恒规律具有一定的理论价值.     

单面完整约束系统的速度依赖对称性与Lutzky守恒量

研究单面完整约束系统的对称性与守恒量.给出单面完整约束系统Lie对称性的定义，得到了由依赖于速度的一般Lie对称性直接导致的Lutzky守恒量，并给出了它的若干特例：有多余坐标的完整约束系统、非保守力学系统、Lagrange系统的Lutzky守恒量.并举例说明结果的应用. 关键词： 分析力学 单面约束 Lie对称性 Lutzky守恒量     

非完整力学系统的Noether-Lie对称性

研究了非完整力学系统的一种新对称性——Noether-Lie对称性及其守恒量. 给出了非完整力学系统Noether -Lie对称性的定义和判据，提出系统的Noether-Lie对称性导致Noether守恒量和广义Hojman守恒量的定理. 举例说明了结果的应用. Hojman守恒量是所给出的广义Hojman守恒量的特例. 关键词： 非完整力学系统 Noether-Lie对称性 Noether守恒量 广义Hojman守恒量     

Magnetic dilaton strings in anti-de Sitter spaces

With an appropriate combination of three Liouville-type dilaton potentials, we construct a new class of spinning magnetic dilaton string solutions which produces a longitudinal magnetic field in the background of anti-de Sitter spacetime. These solutions have no curvature singularity and no horizon, but have a conic geometry. We find that the spinning string has a net electric charge which is proportional to the rotation parameter. We present the suitable counterterm which removes the divergences of the action in the presence of dilaton potential. We also calculate the conserved quantities of the solutions by using the counterterm method.     

Conformal invariance and conserved quantities of a general holonomic system with variable mass

Conformal invariance and conserved quantities of a general holonomic system with variable mass are studied. The definition and the determining equation of conformal invariance for a general holonomic system with variable mass are provided. The conformal factor expression is deduced from conformal invariance and Lie symmetry. The relationship between the conformal invariance and the Lie symmetry is discussed, and the necessary and sufficient condition under which the conformal invariance would be the Lie symmetry of the system under an infinitesimal one-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.     

Definition and relevance of nonequilibrium intensive thermodynamic parameters

We show that intensive thermodynamic parameters associated to additive conserved quantities can be naturally defined from a statistical approach in far-from-equilibrium steady-state systems, under few assumptions, and without any detailed balance requirement. It may apply, e.g., to dissipative systems such as granular gases where volume or mass is still conserved or to systems with periodic boundary conditions where fluxes of conserved quantities are present. We emphasize the usefulness of this concept to characterize the coexistence of different nonequilibrium phases and discuss the influence of the contact between two different systems, in relation with measurement issues.