Spin models as microfoundation of macroscopic market models

Macroscopic price evolution models are commonly used for investment strategies. There are first promising achievements in defining microscopic agent based models for the same purpose. Microscopic models allow a deeper understanding of mechanisms in the market than the purely phenomenological macroscopic models, and thus bear the chance for better models for market regulation. However microscopic models and macroscopic models are commonly studied separately. Here, we exemplify a unified view of a microscopic and a macroscopic market model in a case study, deducing a macroscopic Langevin equation from a microscopic spin market model closely related to the Ising model. The interplay of the microscopic and the macroscopic view allows for a better understanding and adjustment of the microscopic model, as well, and may guide the construction of agent based market models as basis of macroscopic models.     

Testing Super-Deterministic Hidden Variables Theories

We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are uncorrelated, in a super-deterministic hidden variables theory the measurements would be correlated. We estimate that for macroscopic experiments the correlation time is too short to have been noticed yet, but that it may be possible with a suitably designed microscopic experiment to reach a parameter range where one would expect a super-deterministic modification of quantum mechanics to become relevant.     

Basic concepts of synergetics

The paper presents a brief outline of microscopic as well as of macroscopic synergetics. In microscopic synergetics we start from evolution equations for microscopic variables or densities in which fluctuating forces and control parameters are included. When control parameters are changed, the systems are studied close to instability points. The concepts of order parameters, enslaving, critical fluctuations, and critical slowing down are presented. In macroscopic synergetics unbiased estimates on distribution functions and underlying processes are made based on observed moments or correlation functions. In such a case, a Fokker-Planck equation or a corresponding Langevin equation may be derived.     

Connection Structures of Topological Singularity in Micromechanics from a Viewpoint of Generalized Finsler Space

Geometric structures of Cosserat or micropolar continuum are discussed based on geometric objects in a non-Riemannian space. A microrotation is described in a microscopic level than a macroscopic displacement level. In this case, a microscopic rotation can be expressed as a nonlocal internal variable attached to each point in a generalized Finsler space. Such non-local hierarchy is geometrically realized by using a second-order vector bundle viewpoint. Then, two kinds of torsion tensor in the second-order vector bundle are obtained. One is characterized by the macroscopic displacement. The other is characterized by the microscopic rotation. These torsion tensors are equivalent to nonintegrability conditions for multivalued macroscopic displacement and microscopic rotation. Especially, a path dependency of the displacement and the microscopic rotation is represented by a non-vanishing condition of torsion tensors. Moreover, the concept of non-locality of the Finsler geometry implies that the approach of higher-order geometry is applicable to a finite deformation in nonlinear mechanics. The singularity given by the multivalued function is also described as a boundary value problem. An application of the generalized Finsler geometry to a gradient theory is also discussed.     

Quantum microscopic vs. classical macroscopic calculations on the phenomenon of electrostatic influence

In order to compare microscopic and macroscopic approaches to the phenomenon of electrostatic influence, we have studied the atomic charges of an electric conductor, obtained either from macroscopic classical electrostatics, or microscopic quantum ab initio calculations. A torus was chosen as conducting material, built from valence monoelectronic atoms and influenced by an external point charge. The classical electric charges are obtained by integrating the macroscopic density over “atomic" sectors. This density is determined from a numerical integration of linearized electrostatic equations. The quantum charges are defined from Natural Orbitals in MP2/6-31G* calculations on clusters of different sizes. The overall agreement is good, with reasonable discrepancies due (i) to the continuity of the macroscopic model, which ignores the oscillations on atomic distances; and (ii) to the linearity constraint in the macroscopic equations.     

超导电性的量子特征

大量实验事实及量子力学理论已证明微观粒子的运动会表现出一系列量子化特征．因此,过去人们通常认为量子效应是微观粒子所独有的．在本文中,我们通过超导体的一些奇特现象,论述了超导电性的量子特征;阐明在一定条件下由大量微观粒子组成的宏观物体也具有量子化效应,宏观可测量也可以是量子化的,这种宏观量子效应仍可用量子力学理论来研究．     

Quantum teleportation through an entangled state composed of displaced vacuum and single-photon states

We study a teleportation protocol of an unknown macroscopic qubit by means of a quantum channel composed of the displaced vacuum and single-photon states. The scheme is based on linear optical devices such as a beam splitter and photon number resolving detectors. A method based on conditional measurement is used to generate both the macroscopic qubit and entangled state composed from displaced vacuum and single-photon states. We show that such a qubit has both macroscopic and microscopic properties. In particular, we investigate a quantum teleportation protocol from a macroscopic object to a microscopic state. The text was submitted by the author in English.     

脱氧核糖核酸柔性的分子动力学模拟:Amber bsc1和bsc0力场的对比研究

脱氧核糖核酸(DNA)的结构柔性对DNA生物功能的实现具有重要作用,全原子分子动力学模拟是一种研究DNA结构柔性的重要方法.DNA的分子动力学力场在Amber bsc0基础上有了进一步的发展,即Amber bsc1.本文采用基于最新bsc1力场和先前bsc0力场的分子动力学模拟对DNA的宏观柔性和微观柔性进行对比研究,发现力场的改进对DNA宏观柔性参量的预测有一定改善,即所预测的拉伸模量和扭转-伸缩耦合比与实验值更为接近,而弯曲持久长度和扭转持久长度两种力场结果皆与实验值一致.微观分析发现,除了滑移量稍变大,bsc1力场得到的微观结构参量如扭转角和倾斜角与实验值更为接近,且新力场下DNA宏观柔性的改善与DNA的微观结构参量及其涨落紧密相关.     

Macroscopic and microscopic reversibility

The interrelations between (1) the fluctuation-dissipation theorem in conjunction with microscopic reversibility, (2) two principles of macroscopic reversibility, (3) the Casimir-Onsager reciprocal relations, and (4) a macroscopic reciprocity theorem are investigated.     

Second Law of Thermodynamics for Macroscopic Mechanics Coupled to Thermodynamic Degrees of Freedom

Starting from and only using classical Hamiltonian dynamics, we prove the maximum work principle in a system where macroscopic dynamical degrees of freedom are intrinsically coupled to microscopic degrees of freedom. Unlike in many of the standard and recent works on the second law, the macroscopic dynamics is not governed by an external action but undergoes the back reaction of the microscopic degrees of freedom. Our theorems cover such physical situations as impact between macroscopic bodies, thermodynamic machines, and molecular motors. Our work identifies and quantifies the physical limitations on the applicability of the second law for small systems.      

Links between microscopic and macroscopic fluid mechanics

The microscopic and macroscopic versions of fluid mechanics differ qualitatively. Microscopic particles obey time-reversible ordinary differential equations. The resulting particle trajectories {q(t)} may be time-averaged or ensemble-averaged so as to generate field quantities corresponding to macroscopic variables. On the other hand, the macroscopic continuum fields described by fluid mechanics follow irreversible partial differential equations. Smooth particle methods bridge the gap separating these two views of fluids by solving the macroscopic field equations with particle dynamics that resemble molecular dynamics. Recently, nonlinear dynamics have provided some useful tools for understanding the relationship between the microscopic and macroscopic points of view. Chaos and fractals play key roles in this new understanding. Non-equilibrium phase-space averages look very different from their equilibrium counterparts. Away from equilibrium the smooth phase-space distributions are replaced by fractional-dimensional singular distributions that exhibit time irreversibility.     

Microscopic calculation of the constitutive relations

Homogenization theory is used to calculate the macroscopic dielectric constant from the quantum microscopic dielectric function in a periodic medium. The method can be used to calculate any macroscopic constitutive relation, but it is illustrated here for the case of electrodynamics of matter. The so-called cell problem of homogenization theory is solved and an explicit expression is given for the macroscopic dielectric constant in a form akin to the Clausius-Mossotti or Lorentz-Lorenz relation. The validity of this expression is checked by showing that the standard formula is recovered for cubic materials and that the average of the microscopic energy density is the macroscopic one. Finally, the general expression is applied to Bloch eigenstates.     

SOME PROGRESS IN THE LATTICE BOLTZMANN MODEL

A lattice Boltzmann equation model has been developed by using the equilibrium distribution function of the Maxwell－Boltzmann-like form, which is third order in fluid velocity u_α. The criteria of energy conservation between the macroscopic physical quantities and the microscopic particles are introduced into the model, thus the thermal hydrodynamic equations containing the effect of buoyancy force can be recovered in terms of the Taylor and Chapman－Enskog asymptotic expansion methods. The two-dimensional thermal convection phenomena in a square cavity and between two concentric cylinders have been calculated by implementing a heat flux boundary condition. Both numerical results are in good agreement with the conventional numerical results.     

Continuum modeling for two-lane traffic flow with consideration of the traffic interruption probability

Considering the effects that the probability of traffic interruption and the friction between two lanes have on the car-following behaviour,this paper establishes a new two-lane microscopic car-following model.Based on this microscopic model,a new macroscopic model was deduced by the relevance relation of microscopic and macroscopic scale parameters for the two-lane traffic flow.Terms related to lane change are added into the continuity equations and velocity dynamic equations to investigate the lane change rate.Numerical results verify that the proposed model can be efficiently used to reflect the effect of the probability of traffic interruption on the shock,rarefaction wave and lane change behaviour on two-lane freeways.The model has also been applied in reproducing some complex traffic phenomena caused by traffic accident interruption.     

Induced polarization charge density and microscopic local field for a covalent semiconductor

A model calculation of the static macroscopic dielectric function is presented for diamond in which the consequence of the localised and plane wave features of the band structure on the polarizability are separated. Microscopic local field and polarization charge density induced by an uniform external field are analyzed in real space. Although the macroscopic dielectric function is essentially intensitive to small changes in the parameters of the model, microscopic quantities can be rather sensitive suggesting that one should be carefull in constructing a microscopic dielectric matrix to be used in calculating, for instance, phonon frequencies.