Generalized Virial Theorem for Mixed State When Hamiltonians Include Coordinate-Momentum Couplings

The generalized Virial theorem for mixed state, derived from the generalized Hellmann Feynman theorem, only applies to Hamiltonians in which potential of coordinates is separate from momentum energy term. In this paper we discuss Virial theorem for mixed state for some Hamiltonians with coordinate-momentum couplings in order to know their contributions to internal energy.     

Thermal vacuum state for the two-coupled-oscillator model at finite temperature： Derivation and application

Following the spirit of thermo field dynamics initiated by Takahashi and Umezawa, we employ the technique of integration within an ordered product of operators to derive the thermal vacuum state （TVS） for the Hamiltonian H of the two-coupled-oscillator model. The ensemble averages of the system are derived conveniently by using the TVS. In addition, the entropy for this system is discussed based on the relation between the generalized Hellmann-Feynman theorem and the entroy variation in the context of the TVS.     

Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences

There are only a very few known relations in statistical dynamics that are valid for systems driven arbitrarily far-from-equilibrium. One of these is the fluctuation theorem, which places conditions on the entropy production probability distribution of nonequilibrium systems. Another recently discovered far from equilibrium expression relates nonequilibrium measurements of the work done on a system to equilibrium free energy differences. In this paper, we derive a generalized version of the fluctuation theorem for stochastic, microscopically reversible dynamics. Invoking this generalized theorem provides a succinct proof of the nonequilibrium work relation.     

Generalized Hellmann-Feynman Theorem for Ensemble Average Expressed in the Formalism of Pure State Expectation

We show that the generalized Hellmann-Feynman theorem (GHFT) for ensemble average can be expressed in the formalism of pure state expectation. We employ the thermo field dynamics proposed by Umezawa and Takahash to realize this goal, the pure state |0(β)〉 is defined in doubled eigenvector space of the Hamiltonian. Relation between the GHFT and entropy-variation in the context of |0(β)〉 is also derived.     

超细长弹性杆的Mei对称性及其Noether守恒量

基于Kirchhoff的动力学比拟,用动力学的概念和方法研究圆截面弹性杆的Hamilton函数和方程,并给出弹性杆的Mei对称性定义和定理以及定理的证明,最后给出弹性杆动力学系统的Mei对称性导致Noether守恒量的条件及定理,并给出算例. 关键词： 超细长弹性杆 Mei对称性 Noether守恒量     

原子-二聚物分子转化系统在受激拉曼绝热过程中的绝热保真度

从原子-二聚物分子转化系统的非U（1）对称性出发,将保真度的定义推广到了非线性系统.并利用绝热保真度定量地研究了原子-二聚物分子转化系统在受激拉曼绝热过程中的动力学和绝热性.研究发现,这个系统的相干布居俘获态——暗态的绝热保真度作为绝热参量的函数以幂律关系趋于1.这个函数关系与线性系统的绝热参量和绝热保真度的幂律关系非常相似,但该系统的幂指数要远小于线性系统的幂指数.此外,还进一步讨论了如何通过优化受激拉曼绝热过程的外部参量得到更高的绝热保真度,从而优化系统的绝热性,提高原子-分子转化效率. 关键词： 原子-二聚物分子转化系统 暗态 受激拉曼绝热过程 绝热保真度     

约束系统的对称变换

对于用非独立态函数描述的受约束系统,在对称变换下将导致推广的Noether定理,一般说,此时不产生Noether定理的守恒量,在有限约束下内部对称变换的推广Noether定理,就化为通常Noether定理的结果。 关键词：     

On the derivation of the generalized Langevin equation for interacting Brownian particles

The main result of this paper is a derivation of a generalized nonlinear Langevin equation (GLE) forn interacting particles in a bath. A consequence of the derivation is that the exact form of the (generalized) fluctuation-dissipation theorem is obtained. We discuss also the relation between the memory kernel of the GLE and some corresponding correlation functions which can be easily obtained in a molecular dynamics computer experiment. In the same spirit it is shown that the approach applies to a Brownian particle subjected to a stationary external field. The technique presented in a previous paper to simulate generalized Brownian dynamics can be easily extended to the present case. Our derivation intends to clarify the uses and (possibly) abuses of the Langevin equation in Brownian dynamics studies.     

Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control

A new kind of generalized synchronization of two chaotic systems with uncertain parameters is proposed. Based on a pragmatical asymptotical stability theorem and an assumption of equal probability for ergodic initial conditions, an adaptive control law is derived so that it can be proved strictly that the common null solution of error dynamics and of parameter dynamics is actually asymptotically stable, i.e. these two identical systems are in generalized synchronization and the estimated parameters approach the uncertain values. It is called pragmatical generalized synchronization. Finally, two numerical examples are studied for two Quantum-CNN oscillator chaotic systems to show the effectiveness of the proposed generalized synchronization strategy with a double Duffing chaotic system as a goal system.     

对称Anderson晶格基态的局域方法近似

本文采用格林函数技术,计算了对称Anderson晶格的H-F基态能量,然后采用局域方法近似,计算了相关能、相关基态能量、局域磁矩、电荷涨落和自旋涨落。使用平方态密度,得到了解析表达式。结果表明,当同一格点的f-f库仑相互作用U减小或d-f杂化强度V增大,局域磁矩变小。 关键词：     

Generalized two-mode thermal vacuum state for the Hamiltonian of a parametric amplifier derived by the IWOP method

In this paper, we employ the technique of integration within an ordered product of operators (IWOP) to derive a generalized two-mode thermal vacuum state (GTTVS) for the Hamiltonian of a parametric amplifier. Application of GTTVS in calculating the ensemble average is discussed. The result is in agreement with that obtained by using the generalized Hellmann-Feynmann theorem.     

The Fluctuation Theorem as a Gibbs Property

Common ground to recent studies exploiting relations between dynamical systems and nonequilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti–Cohen fluctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz–Spohn analysis of this fluctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the fluctuation theorem as a Gibbs property, as it follows from the very definition of Gibbs state. We give a local version of the fluctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics.     

The sampling theorem and coherent state systems

The Poisson Summation Formula and the sampling theorem for band limited signals, well known in the context of Fourier transformation theory, are analyzed from the perspective of the Zak basis and coherent state systems associated with the Heisenberg-Weyl group. In particular, we rephrase the content of the sampling theorem in terms coherent states and show that this in turn permits extensions, which allow us to make specific statements concerning standard and generalized coherent state systems on von Neumann or finer lattices. The text was submitted by the author in English.     

A general framework for non-equilibrium phenomena: the master equation and its formal consequences

We consider non-equilibrium systems defined by a state space, and by a stochastic dynamics and its stationary state. The dynamics need not satisfy detailed balance. In this abstract framework we do the following: (1) define and analyze “relative entropy”, (2) study dissipation in the relaxation to the stationary state, as well as the extra dissipation to maintain the system in its stationary state against some detailed balance dynamics, (3) extend the fluctuation-dissipation theorem and the Onsager relations, and (4) give a formula for the stationary state in terms of a summation over trees.     

推广的Thomas－Fermi方法中适用的新式核密度

给出一种适用于推广的Ｔｈｏｍａｓ－Ｆｅｒｍｉ方法（ＥＴＦ）的密度形式．取ＳｋＭ势参量，对几个球形核的基态性质进行了计算，结果优于通常采用的多参数密度形式．用期望值方法（ＥＶＭ）给出的基态能量能重现Ｈ—Ｆ的计算结果．     

Return to equilibrium and stability of dynamics (semigroup dynamics case)

A study is presented of asymptotically normal dynamical semigroups for which there exists a faithful normal state satisfying the detailed balance condition. Such dynamics reveals a return to a stationary state if additionally a weak cluster property is assumed. The generalized stability condition and generalized wave operators are introduced. The theory is illustrated by models.     

Linear response and fluctuation theorems for nonstationary stochastic processes

Linear response theory is developed for nonstationary Markov processes. A generalized fluctuation theorem is derived which relates the response function to a correlation of fluctuations of the unperturbed nonstationary process. It is shown that it reduces to an ordinary fluctuation theorem relating the response function to the two-point correlation between fluctuations of state variables in the case of a Gaussian distribution function. The results are illustrated by explicit calculation for the class of nonstationary linear Fokker-Planck processes.Supported by Schweizerischer Nationalfonds.     

The interaction of light with a semiinfinite dielectric as a phonon problem; the generalized Snellius law and Fresnel formulae

Using Ewald's formulae it is possible to evaluate the electromagnetic field generated by a mechanical plane wave propagating through a semiinfinite dipole crystal. The problem of refraction and reflection of an external electromagnetic wave on a semiinfinite dipole crystal is thus reduced to the evaluation of the forced vibrations of this crystal excited by the incident electromagnetic wave. Applying this approach, the generalized Snellius law and generalized Fresnel formulae can be deduced. In the limit of long waves these general formulae change into the usual classical expressions. The Ewald extinction theorem follows directly from the lattice dynamics of our system.     

Microdynamics and nonlinear stochastic processes of gross variables

Starting from classical Hamiltonian mechanics, we derive for the dynamics of gross variables in nonequilibrium systems exact nonlinear generalized Fokker-Planck and Langevin equations in which the effect of the initial preparation is taken into account explicitly. This latter concept allows for the construction of a uniquely determined projection operator. The memory functions occurring in the Langevin equations are related to the random forces by a fluctuation-dissipation theorem of the second kind. We discuss the connection with the generalized Fokker-Planck equation. The known results for equilibrium fluctuations are recovered as a special case.Supported in part by the National Science Foundation, Grant CHE78-21460.