核温度的动力学计算

介绍了测量热力学微正则系综中哈密顿动力学系统温度的一种新的动力学途径,即在各态历经性的假设下,温度可作为函数（Ｈ／‖Ｈ‖２）在能量面上的时间平均算出．这一方法不仅给出了确定温度的一种有效的计算途径,而且也提供了动力学系统理论和哈密顿系统的统计力学之间的内在联系． A new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the microcanonical ensemble of thermodynamics is presented. It shows that under the hypothesis of ergodicity the temperature can be computed as a time average of the function, ·(H/‖H‖ 2) , on the energy surface. This method not only yields an efficient computational approach for determining the temperature, but also provides an intrinsic link between dynamical system theory and the statistical...     

Entropy increase for a class of dynamical maps

The dynamical evolution of a quantum system is described by a one parameter family of linear transformations of the space of self-adjoint trace class operators (on the Hilbert space of the system) into itself, which map statistical operators to statistical operators. We call such transformations dynamical maps. We give a sufficient condition for a dynamical map A not to decrease the entropy of a statistical operator. In the special case of an N-level system, this condition is also necessary and it is equivalent to the property that A preserves the central state.     

Turning point properties as a method for the characterization of the ergodic dynamics of one-dimensional iterative maps

Dynamical as well as statistical properties of the ergodic and fully developed chaotic dynamics of iterative maps are investigated by means of a turning point analysis. The turning points of a trajectory are hereby defined as the local maxima and minima of the trajectory. An examination of the turning point density directly provides us with the information of the position of the fixed point for the corresponding dynamical system. Dividing the ergodic dynamics into phases consisting of turning points and nonturning points, respectively, elucidates the understanding of the organization of the chaotic dynamics for maps. The turning point map contains information on any iteration of the dynamical law and is shown to possess an asymptotic scaling behaviour which is responsible for the assignment of dynamical structures to the environment of the two fixed points of the map. Universal statistical turning point properties are derived for doubly symmetric maps. Possible applications of the observed turning point properties for the analysis of time series are discussed in some detail. (c) 1997 American Institute of Physics.     

Multifragmentation of charge asymmetric nuclear systems

The multifragmentation of excited spherical nuclear sources with various N/Z ratios and fixed mass number is studied within dynamical and statistical models. The dynamical model treats the multifragmentation process as a final stage of growth of density fluctuations in unstable expanding nuclear matter. The statistical model makes a choice of the final multifragment configuration according to its statistical weight at a global thermal equilibrium. Similarities and differences in the predictions of the two models on the isotopic composition of the produced fragments are presented and the most sensitive observable characteristics are discussed.     

Leading Order Response of Statistical Averages of a Dynamical System to Small Stochastic Perturbations

The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes.     

用动力学方法研究原子分子碰撞过程中的统计平均问题

动力学李代数方法在研究原子分子碰撞问题中是一种很重要的方法.在计算过程中我们用密度算子导出了物理量的统计平均值.同时我们用时间演化算子计算了振转能量的跃迁几率.作为例子我们用此方法计算了H2和He的碰撞问题.     

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.     

Even and Odd Coherent States for Time-Dependent Harmonic Oscillator

The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach.     

Chance and Chandra

A few examples are given of Chandra’s work on statistical and stochastic problems that relate to open questions in astrophysics, in particular his theory of dynamical relaxation in systems with inverse-square interparticle forces. The roles of chaos and integrability in this theory require clarification, especially for systems having a dominant central mass. After this prelude, a hypothetical form of bosonic dark matter with a simple but nontrivial statistical mechanics is discussed. This makes for a number of eminently falsifiable predictions, including some exotic consequences for dynamical friction.     

Correlation integral as a tool for distinguishing between dynamics and statistics in time series data

We propose a new test for time series data for proper choice of processing technique: dynamical or statistical. It is based upon the normalized slope of the correlation integral (, m) = m⁻¹d(ln C()) /d ln , where m is the embedding dimension. It is shown that when does not tend to 0 on the resolved range of scales as m grows, then there will be serious limitations for dynamical methods even if the data are dynamical by nature. In the latter case it means that the length of time series does not allow to resolve small scales, and on large scales the delay reconstruction for any m mixes true and false neighbours of points and therefore restricts the application of dynamical techniques, such as estimating Lyapunov exponents or predicting time series.     

Derivation of the statistical model of nuclear reactions from the theory of stationary irreversible processes

Nuclear reactions via a compound nucleus are considered as an example of the quantum theory of stationary irreversible processes. A density matrix formalism with Liouville space methods is developed, including in a natural way the dynamical and statistical aspects of nuclear reactions. For densely spaced compound levels the statistical model is obtained as a limiting case.     

Emerging of Stochastic Dynamical Equalities and Steady State Thermodynamics from Darwinian Dynamics

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.     

Chern–Simons theory, 2d Yang–Mills, and Lie algebra wanderers

The dynamically triangulated random surface (DTRS) approach to Euclidean quantum gravity in two dimensions is considered for the case of the elemental building blocks being quadrangles instead of the usually used triangles. The well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation are adapted to the problem of these dynamical quadrangulations. The thus defined ensemble of 4-valent graphs is appropriate for coupling to it the 6- and 8-vertex models of statistical mechanics. Using a series of extensive Monte Carlo simulations and accompanying finite-size scaling analyses, we investigate the critical behaviour of the 6-vertex F model coupled to the ensemble of dynamical quadrangulations and determine the matter related as well as the graph related critical exponents of the model.     

Estimating statistics for detecting determinism using global dynamical models

Classification of time series using a dynamical system ansatz is potentially powerful, however assessing performance for noisy experimental data is problematic. Here, we develop a rigorous statistical framework for calculating classification probabilities using global dynamical models, and analytically derive some asymptotic properties. We illustrate the method numerically by attempting to detect “determinism” in a noisy data set.     

Effective actions for statistical data assimilation

Data assimilation is a problem in estimating the fixed parameters and state of a model of an observed dynamical system as it receives inputs from measurements passing information to the model. Using methods developed in statistical physics, we present effective actions and equations of motion for the mean orbits associated with the temporal development of a dynamical model when it has errors, there is uncertainty in its initial state, and it receives information from noisy measurements. If there are statistical dependences among errors in the measurements they can be included in this approach.     

Dynamical thermostatting and statistical ensembles

Dynamical thermostatting constitutes a procedure for computing thermodynamical mean values of classical dynamical systems that is of interest both from the practical and from the conceptual points of view. Here we extend and unify previous partial results, showing that the dynamical thermostatting approach can be implemented in order to simulate a wide family of statistical ensembles of general dynamical systems with a vanishing divergence and admitting an integral of motion. As a particular illustration, the thermostatting procedure is applied to power law-like maximum entropy ensembles.     

Dynamics and Thermodynamics of Layered Neural Network

We consider the dynamics of overlaps in a layered network with tanhβ(χ) as its threshold transfer function. The analysis of dynamical stability shows that when the external stimulus is close enough to one of the stored patterns the retrieval state becomes globally stable. The statistical mechanics of the same model, in which the parameter β is introduced as thermal noise, is also studied. We find that the thermodynamical stability is equivalent to the dynamical stability.     

Landauer's principle and the conservation of information

Erasure of information requires the dissipation of a minimal amount of energy as being formulated in Landauer's principle. This profound concept in information processing has recently been derived by use of basic dynamical principles of statistical mechanics. We present an alternative derivation of Landauer's principle based on dynamical principles and certain properties of the Shannon–Gibbs–Boltzmann entropy, in particular, (sub-)additivity.