The valence-bond representation of the three dimensional antiferromagnetic Heisenberg model

We present results on the specific heat and the staggered magnetization of the three dimensional antiferromagnetic Heisenberg model. These results are obtained from a numerical solution of the approximated evolution equation for the expectation values of the Boltzmann factor between valence-bond states.     

模糊自整定比例积分控制在空间三维纳米定位台的应用

介绍了一种空间三自由度纳米定位平台,其应用背景为光刻投影物镜波像差检测系统的精密对准,因此对定位精度和定位速度都提出了很高的要求。首先简要介绍了空间三维纳米定位台;然后将模糊控制同传统PI(比例积分)控制相结合,利用定位偏差和偏差变化率信息,通过模糊推理实时调整PI控制参数,并在VC++环境下实现了模糊自整定PI参数的控制算法。实验结果表明,该控制方法较常规PI控制器能够有效地提高响应速度,减小阶跃响应超调量,保证了控制的实时性。     

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations. Received: 27 April 1998 / Revised: 2 September 1998 / Accepted: 10 September 1998     

Current algebra representation for the 3+1 dimensional Dirac-Yang-Mills theory

The structure of the current algebra representation in the state space of fermions in an external Yang-Mills field in 3+1 space-time dimensions is analyzed; the topology of the vector space is determined by a countable family of semi-definite inner products. We show that there is no hermitian non-trivial Hilbert space representation such that the energy is bounded from below. The structure of the Hilbert space for the quantized coupled Dirac-Yang-Mills system is discussed and the existence of the vacuum vector and the cancellation of commutator anomalies is described in terms of complex line bundles over infinite-dimensional Grassmannians.     

Ag309团簇升温过程中结构转变的分子动力学模拟研究

采用分子动力学模拟研究了具有面心立方(fcc)晶格结构的截断八面体Ag309团簇升温过程中结构演变.对团簇的能量曲线变化、快照图演变和键对分析表明:无缺陷截断八面体Ag309团簇在410 K时转变为二十面体,在840 K时熔化;不同缺陷诱导二十面体结构转变温度异常变化,沿晶面滑移缺陷使二十面体转变温度升高,沿晶面旋转缺陷使二十面体结构转变温度降低;不同缺陷对团簇键型和势能产生的影响是使二十面体结构转变温度异常变化的主要诱导因素.这种通过缺陷控制团簇结构转变的研究为新型纳米结构的可控制备提供理论基础.     

Molecular dynamics simulation of a model for (one-dimensional) structural phase transitions

Molecular dynamics computer simulations have been carried out for a structurally unstable 1-D lattice, having a double well local potential and nearest neighbor coupling. The results show pronounced domain structure at low temperature — a feature not to be found in mean field or anharmonic phonon perturbation theories. Quantitative comparison is made with the analysis of Krumhansl and Schrieffer, which predicts this behavior.     

Majorana表象下的纠缠动力学

借助在Majorana表象下提出的纠缠度定义, 研究了对称双阱中两个玻色原子组成的系统的纠缠动力学. 得到了系统的任意态在Majorana 表象下的表示, 并考察了原子间相互作用及系统初始状态对纠缠度动力学的影响. 发现原子间相互作用会决定纠缠度振荡的频率, 而纠缠度振荡的幅度对系统的初态很敏感.     

Physical consequences of a nonparametric uncertainty model in structural dynamics

One of the main claims of the nonparametric model of random uncertainty introduced by Soize (2000) [3] is its ability to account for model uncertainty. The present paper investigates this claim by examining the statistics of natural frequencies, total energy and underlying dispersion equation yielded by the nonparametric approach for two simple systems: a thin plate in bending and a one-dimensional finite periodic mass–spring chain. Results for the plate show that the average modal density and the underlying dispersion equation of the structure are gradually and systematically altered with increasing uncertainty. The findings for the mass–spring chain corroborate the findings for the plate and show that the remote coupling of nonadjacent degrees of freedom induced by the approach suppresses the phenomenon of mode localization. This remote coupling also leads to an instantaneous response of all points in the chain when one mass is excited. In the light of these results, it is argued that the nonparametric approach can deal with a certain type of model uncertainty, in this case the presence of unknown terms of higher or lower order in the governing differential equation, but that certain expectations about the system such as the average modal density may conflict with these results.     

Two time scales and violation of the fluctuation-dissipation theorem in a finite dimensional model for structural glasses

We study the breakdown of fluctuation-dissipation relations between time-dependent density-density correlations and associated responses following a quench in the chemical potential in the frustrated Ising lattice gas. The corresponding slow dynamics is characterized by two well-separated time scales characterized by a constant value of the fluctuation-dissipation ratio. This result is particularly relevant since activated processes dominate the long-time dynamics of the system.     

Phase space representation of quantum dynamics

We discuss a phase space representation of quantum dynamics of systems with many degrees of freedom. This representation is based on a perturbative expansion in quantum fluctuations around one of the classical limits. We explicitly analyze expansions around three such limits: (i) corpuscular or Newtonian limit in the coordinate-momentum representation, (ii) wave or Gross-Pitaevskii limit for interacting bosons in the coherent state representation, and (iii) Bloch limit for the spin systems. We discuss both the semiclassical (truncated Wigner) approximation and further quantum corrections appearing in the form of either stochastic quantum jumps along the classical trajectories or the nonlinear response to such jumps. We also discuss how quantum jumps naturally emerge in the analysis of non-equal time correlation functions. This representation of quantum dynamics is closely related to the phase space methods based on the Wigner-Weyl quantization and to the Keldysh technique. We show how such concepts as the Wigner function, Weyl symbol, Moyal product, Bopp operators, and others automatically emerge from the Feynmann's path integral representation of the evolution in the Heisenberg representation. We illustrate the applicability of this expansion with various examples mostly in the context of cold atom systems including sine-Gordon model, one- and two-dimensional Bose-Hubbard model, Dicke model and others.     

A structural model of market dynamics,and why it matters

In this paper, we explore an approach to understanding price fluctuations within a market via considerations of functional dependencies between asset prices. Interestingly, this approach suggests a class of models of a type used earlier to describe the dynamics of real and artificial neural networks. Statistical physics approaches turn out to be suitable for an analysis of their collective properties. In this paper, we first motivate the basic phenomenology and modelling arguments before moving on to discussing some major issues with inference and empirical verification. In particular, we focus on the natural creation of market states through the inclusion of interactions and how these then interfere with inference. This is primarily addressed in a synthetic setting. Finally we investigate real data to test the ability of our approach to capture some key features of the behaviour of financial markets.     

Nuclear dynamics with a wavelet representation

Fluctuation-dissipation aspects in heavy-ion reactions at intermediate energies are addressed in the framework of the DYWAN model. This new approach provides a strongly compressed representation of nuclear systems by expanding the corresponding wavefunctions in a basis of wavelets. Comparisons with the experimental results in nucleus—nucleus and nucleon—nucleus reactions are performed. These preliminary results provide a good test of working for the model and open new perspectives in the modeling of nuclear reactions.     

Cosmological dynamics in tomographic probability representation

The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The evolution of the universe state is described by standard positive transition probability (tomographic transition probability) instead of the complex transition probability amplitude (Feynman path integral) of the standard approach. The latter one is expressed in terms of the tomographic transition probability. Examples of minisuperspaces in the framework of the suggested approach are presented. Possibility of observational applications of the universe tomographs are discussed.     

Deterministic single-file dynamics in collisional representation

We re-examine numerically the diffusion of a deterministic, or ballistic single file with preassigned velocity distribution (Jepsen's gas) from a collisional viewpoint. For a two-modal velocity distribution, where half the particles have velocity +/-c, the collisional statistics is analytically proven to reproduce the continuous time representation. For a three-modal velocity distribution with equal fractions, where less than 12 of the particles have velocity +/-c, with the remaining particles at rest, the collisional process is shown to be inhomogeneous; its stationary properties are discussed here by combining exact and phenomenological arguments. Collisional memory effects are then related to the negative power-law tails in the velocity autocorrelation functions, predicted earlier in the continuous time formalism. Numerical and analytical results for Gaussian and four-modal Jepsen's gases are also reported for the sake of a comparison.     

量纲分析的线性代数方法

把量纲概念与矢量空间联系起来,提出用线性代数进行量纲分析的方法,并举例说明。     

Three dimensional dynamics of ferromagnetic swimmer

It is shown that a flexible ferromagnetic filament self-propels perpendicularly to the AC magnetic field during a limited period of time due to the instability of the planar motion with respect to three dimensional perturbations. The transition from the oscillating U-like shapes to the oscillating S-like shapes is characterized by the calculated Wr number.     

A model for two dimensional orientational order

We use a generalization of Kikuchi's cluster variational method (CVM), in the pair approximation, to study anisotropic plane rotors on a square lattice as a simple model for two dimensional nematics. The system was shown to exhibit nematic ordered states at low temperature, disordering, for all anisotropies, through a continuous transition. The orientational distribution functions, order parameter, internal energy and specific heat were calculated within the CVM and compared with the results of a recent computer simulation. Estimates for the non-classical exponents were obtained using a mean field renormalization group analysis. A spin wave argument was also used to investigate the role of long range fluctuations near the isotropic fixed point. The accuracy of these different techniques is discussed within the context of our model.     

New representation for energy-momentum and its applications to relativistic dynamics

In this paper we introduce the concept counterpart of rapidity and define energy and momentum of the relativistic particle as functions of the counterpart of rapidity. Formulae of the relativistic mechanics defined in such a way are regular near the zero-mass and speed of light state. This representation admits to attain a correct limit of the formulae of the relativistic mechanics, including the Dirac equation, at zero-mass point and explains violation of the parity at this state. On the other hand, the representation for energy-momentum can be realized as a mapping from the massless state onto the massive one which looks like a “q deformation”. Hypothesis on quantization of the energy-momentum and the velocity near the light speed is suggested. The group of transformations using the counterpart of rapidity as a parameter of transformation is constructed.