广义经典力学系统的对称性与Mei守恒量

研究广义经典力学系统的对称性和一类新型守恒量——Mei守恒量.在高维增广相空间中建立 了系统的运动微分方程；给出了系统的Mei对称性、Noether对称性和Lie对称性的判据；得 到了分别由三种对称性导致Mei守恒量的条件和Mei守恒量的形式.举例说明结果的应用. 关键词： 广义经典力学 Mei对称性 Noether对称性 Lie对称性 守恒量     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

Noether-Form Invariance of Nonholonomic Controllable Mechanical Systems in Phase Space

In this paper, we study the Noether-form invariance of nonholonomic mechanical controllable systems in phase space. Equations of motion of the controllable mechanical systems in phase space are presented. The definition and the criterion for this system are presented. A new conserved quantity and the Noether conserved quantity deduced from the Noether-form invariance are obtained. An example is given to illustrate the application of the results.     

相空间中单面完整约束力学系统的对称性与守恒量

在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程；给出了系统的Norther对称性，Lie对称性和Mei对称性的判据；研究了三种对称性之间的关系；得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量，研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用. 关键词： 分析力学 单面约束 对称性 守恒量 相空间     

Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations

This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.     

Conformal invariance and conserved quantities of general holonomic systems in phase space

This paper studies the conformal invariance and conserved quantities of general holonomic systems in phase space. The definition and the determining equation of conformal invariance for general holonomic systems in phase space 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 that the conformal invariance would be the Lie symmetry of the system under the infinitesimal single-parameter transformation group is deduced. The conserved quantities of the system are given. An example is given to illustrate the application of the result.     

Theoretical results concerning the influence of non‐random‐field defects

We shall focus on extended defect systems and review their critical behavior. Primarily, with two aims, one of which is to understand phase transitions and how to derive effective dimension of extended defects with various structures, and the other is to propose a new research-method for defect systems, we let extended defects grow on a triangular lattice with frustration in a similar fashion to diffusion-limited aggregation, and discuss the situation. The existence of phase transitions, phase diagram, effective defect dimension, etc. will be shown. Furthermore, we shall summarize theoretical studies of extended defect systems on phase diagrams, critical behavior, tricritical behavior, and crossover behavior as static properties, and on nonconserved systems and conserved systems as dynamic properties.     

相空间中二阶线性非完整系统的形式不变性

研究相空间中二阶线性非完整系统的形式不变性.给出相空间中二阶线性非完整系统形式不变性的定义和判据，得到形式不变性的结构方程和守恒量的形式，并举例说明结果的应用. 关键词： 相空间 二阶线性非完整系统 形式不变性 守恒量     

相空间中变质量力学系统的Hojman守恒量

研究一般的无限小变换下相空间中变质量力学系统Lie对称性的Hojman守恒量. 给出了相空 间中变质量力学系统Lie 对称性的确定方程和Hojman守恒量定理,并举例说明结果的应用. 关键词： 相空间 变质量系统 一般的无限小变换 Lie对称性 Hojman守恒量     

Conservative ensembles for nonequilibrium lattice-gas systems

We show how to set up a constant particle ensemble for the steady state of nonequilibrium lattice-gas systems which originally are defined on a constant rate ensemble. We focus on nonequilibrium systems in which particles are created and annihilated on the sites of a lattice and described by a master equation. We consider also the case in which a quantity other than the number of particle is conserved. The conservative ensembles can be useful in the study of phase transitions and critical phenomena particularly discontinuous phase transitions.     

Kinetics of Phase Transitions

We review developments in the field of phase ordering dynamics, viz., the evolution of a homogeneous multi-component mixture which has been rendered thermodynamically unstable by a rapid quench below the critical temperature. We discuss results for cases with both nonconserved and conserved order parameters. We also highlight recent research directions in this field, i.e., the incorporation of experimentally relevant effects in the studies of phase ordering systems.     

Quantum phase transitions and conserved charges

The constraints on the scaling properties of conserved charge densities in the vicinity of a zero temperature (T), second-order quantum phase transition are studied. We introduce a generalized Wilson ratio, characterizing the nonlinear response to an external field,H, coupling to any conserved charge, and argue that it is a completely universal function ofH/T: this is illustrated by computations on model systems. We also note implications for transitions where the order parameter is a conserved charge (as in aT=0 ferromagnet-paramagnet transition).     

Transformation properties of a constrained hamiltonian system and PBRST charge

We derive a generalized first Noether theorem for weakly quasi-invariant systems with singular higher-order Lagrangians, subject to the extra constraints and generalized Noether identities for a variant system in phase space. The strong and weak conservation laws for variant systems are also deduced. Some preliminary applications to field theories are given. In certain cases a variant system is also a constrained Hamiltonian system. A PBRST (weak) conserved charge is obtained that differs from the usual BRST charge.     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

Conformal Invariance and a New Type of Conserved Quantities of MechanicalSystems with Variable Mass in Phase Space

Conformal invariance and a new type of conserved quantities of mechanical systems with variable mass in phase space are studied. Firstly, the definition and determining equation of conformal invariance are presented. The relationship between the conformal invariance and the Lie symmetry is given, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry under the infinitesimal transformations is provided.Secondly, a new type of conserved quantities of the conformal invariance are obtained by using the Lie symmetry of the system. Lastly, an example is given to illustrate the application of the results.     

New Type of Conserved Quantities of Lie Symmetry for Nonholonomic Mechanical Systems in Phase Space

The new types of conserved quantities, which are directly induced by Liesymmetry of nonholonomic mechanical systems in phase space, are studied. Firstly, the criterion of the weak Lie symmetry and the strong Lie symmetry are given. Secondly, the conditions of existence of the new type of conserved quantities induced by the weak Lie symmetry and the strong Lie symmetry directly are obtained, and their form is presented. Finally, an Appell-Hamel example is discussed to further illustrate the applications of the results.     

Systems of Covariance in Relativistic Quantum Mechanics

Developing some earlier work for spin-zerosystems found in the literature, we use some recentlyobtained generalized systems of covariance for thePoincare group to suggest a method for definingcovariant localization operators on phase space formassive relativistic particles with arbitrary integralor half-integral spins. These operators lead tooperationally defined position operators on spacelikehyperplanes, which turn out to be the Newton-Wigneroperators, and, as in the earlier results on spin-zerosystems, admit a consistent probability interpretationwith conserved currents.     

Noise induced patterning in periodic systems with conserved dynamics

We study pattern formation in periodic systems with conserved dynamics driven by both thermally sustained flux and external (athermal) flux. Assuming the stochastic nature of each kind of flux we discuss noise induced patterning with competing stochastic dynamics in the framework of the modulated phase field method. Analytical results obtained within the mean field theory are compared with computer simulations.     

On the broken time translation symmetry in macroscopic systems: Precessing states and off-diagonal long-range order

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time translation symmetry is observable only if the charge Q is not strictly conserved and may decay. This dichotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ _Q of the charge Q and the energy relaxation time τ _E . If τ _Q ? τ _E , the perturbed system relaxes first to the state with the ODLRO, which persists for a long time and finally relaxes to the full equilibrium static state. In the limit τQ → ∞, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time translation symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid ⁴He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.     

A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems

A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied. The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.