Glauber dynamics of fluctuations

We derive the time evolution of the normal fluctuations of a classical lattice spin system induced by a generalized Glauber dynamics. The canonical form of this dynamics is derived. We prove that it is asymptotically (i.e., after the central limit) free. The results are applied to give a rigorous proof of the macroscopic reciprocity relations and the linear theory for small deviations from equilibrium.     

Linear Response Theory for Thermally Driven Quantum Open Systems

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes in thermally driven quantum open systems. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [V. Jakšić Y. Ogata and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.].     

Generalized Weierstrass Relations and Frobenius Reciprocity

This article investigates local properties of the further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M from the viewpoint of the study of submanifold quantum mechanics. We show that the kernel of a certain Dirac operator defined over S, which we call a submanifold Dirac operator, gives the data of the immersion. In the derivation, the simple Frobenius reciprocity of Clifford algebras S and M plays an important role.      

Development of an electronic stopping power model based on deep learning and its application in ion range prediction

Deep learning algorithm emerges as a new method to take the raw features from large dataset and mine their deep implicit relations, which is promising for solving traditional physical challenges. A particularly intricate and difficult challenge is the energy loss mechanism of energetic ions in solid, where accurate prediction of stopping power is a long-time problem. In this work, we develop a deep-learning-based stopping power model with high overall accuracy, and overcome the long-standing deficiency of the existing classical models by improving the predictive accuracy of stopping power for ultra-heavy ion with low energy, and the corresponding projected range. This electronic stopping power model, based on deep learning algorithm, could be hopefully applied for the study of ion-solid interaction mechanism and enormous relevant applications.     

Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

Berry and Klein [J. Mod. Opt. 43, 2139-2164 (1997)] showed that the Talbot effects in classical optics are naturally expressed by Gauss sums in number theory. Their result was obtained by a computation of Helmholtz equation. In this article, we calculate the effects using Fresnel integral and show that the result is also represented by Gauss sums. However function forms of these two computational results are apparently different. We show that the reciprocity law of Gauss sums connects these results and both completely agree with. The Helmholtz equation can be regarded as an equation based upon wavy nature in optics whereas the Fresnel integral is defined by a sum over the paths based upon a particle picture in optics. Thus the agreement of these two computational results could be interpreted in terms of the concept of the wave-particle complementarity, though the concept is for quantum mechanical phenomenon. This interpretation leads us to a relation between the reciprocity of Gauss sums in number theory and the wave-particle complementarity in wave physics. We discuss it in detail.     

An Investigation of the Reciprocity Principle of Light Exposures Using Microfading Spectrometry

It is frequently assumed that sensitive museum materials follow the reciprocity principle of light exposures. Thus, equivalent exposure doses obtained by using either high-illuminance levels for short periods of time or lower illumination for longer exhibition periods are believed to cause similar degrees of damage to an object. Microfading spectrometry permitted the investigation of this phenomenon by evaluation of light-induced changes in a series of samples. The effects of equivalent exposure doses on materials such as Blue Wool 1, LightCheck Ultra, and various dyed silks from a reference collection were compared. The results indicate that reciprocity is obeyed by the most stable colorants, while materials with lower stability to light may experience deviations that are proportional to the intensity of illumination. This study confirms that reciprocity failure is associated with the use of high-intensity lamps during accelerated-aging trials. Therefore only those tests conducted at low-illumination intensity ranges where reciprocity holds should be employed when one estimates the extent of damage occurring in a museum environment.     

格林互易定理在求解均匀带电圆环的静电势分布中的应用

对于静电场,由普遍的格林互易定理得出特殊情形下的格林互易定理.应用该定理推导出均匀带电圆环的数种在形式上互不相同的静电势分布解式.     

Onsager Relations and Eulerian Hydrodynamic Limit for Systems with Several Conservation Laws

We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager's reciprocity relations must hold. We check validity of these identities whenever a stationary measure with product structure exists. It also follows that, as a general rule, the equilibrium thermodynamic entropy (as function of the densities of the conserved variables) is a globally convex Lax entropy of the hyperbolic systems of conservation laws arising as hydrodynamic limit. As concrete examples we also present a number of models modeling deposition (or domain growth) phenomena. The Onsager relations arising in the context of hydrodynamic limits under hyperbolic scaling seem to be novel. The fact that equilibrium thermodynamic entropy is Lax entropy for the arising Euler equations was noticed earlier in the context of Hamiltonian systems with weak noise, see ref. 7.     

Duality in physical sciences and beyond

An extended meaning of duality is suggested in the context of development of major themes in physical sciences since Newton. In such a generalization,five distinct aspects of duality are sought to be identified and illustrated through concrete examples drawn from various physical concepts, old and new. These are (i) reciprocity, (ii) parallelism, (iii) alternative formulation, (iv) unification and (v) measurement incompatibility. Bohr’s view of duality and the Copenhagen Interpretation are discussed briefly in this context. Finally, duality aspects beyond physics are briefly touched upon, the philosophical link being provided by Bohr’s Complementarity Principle on the one hand, and recent attempts (notably by Capra) to draw suggestive parallels between modern science and Eastern mysticism on the other. “Be in truth eternal, beyond earthly opposites”—Bhagwat Gita. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicate this paper to him on this occasion.     

Generalizing Planck’s distribution by using the Carati–Galgani model of molecular collisions

Classical systems of coupled harmonic oscillators are studied using the Carati–Galgani model. We investigate the consequences for Einstein’s conjecture by considering that the exchange of energy in molecular collisions follows the Lévy type statistics. We develop a generalization of Planck’s distribution admitting that there are analogous relations in the equilibrium quantum statistical mechanics of the relations found using the nonequilibrium classical statistical mechanics approach. The generalization of Planck’s law based on the nonextensive statistical mechanics formalism is compatible with our analysis.     

两个相邻目标对平面波、高斯波束的光散射

基于等效原理和互易性定理研究了两个靠近目标对平面波、高斯波束的光散射问题,给出了这一复合光散射模型的二阶散射结果。通常一阶散射结果容易求解,但由于耦合效应的复杂性,很难给出二阶散射结果的解析形式。为了解决这一问题,应用互易性定理给出了求解任意相邻介质目标二阶散射场的公式,同时借助等效原理将求解散射场公式中的体积分简化为面积分的形式,从而降低了求解难度。求解了两相邻球形粒子的复合散射场,并将求解结果与应用时域积分方程法求得的结果进行了比较。同时,还讨论了束腰半径、目标位置对散射截面及偏振度的影响。     

Integral Method o Reciprocity in the Spectroscopy of Laser Crystals with Impurity Centers

A new method of determining the stimulated emission cross-section spectra from the absorption cross-section spectra, which we call the integral method of reciprocity, is suggested it does not require knowledge of the structure of the impurity-center electron levels. Based on this method, formulas for calculating the radiation lifetime of impurity centers in crystals have been derived. The effectiveness of the integral method of reciprocity was demonstrated in determining the stimulated emission cross sections and radiation lifetime of an ytterbium ion in the laser crystals Yb³⁺:KYW and Yb³⁺:KGW.     

等效原理和互易性定理在两个相邻球形目标电磁散射中的应用

基于等效原理和互易性定理研究了两个相邻目标的电磁散射问题，给出了这一复合电磁散射模型的二阶散射结果. 通常平面入射波的一阶散射结果容易求解，但由于耦合效应的复杂性，很难给出二阶散射结果的解析形式. 应用互易性定理给出了求解任意相邻导体/介质目标二阶电磁散射场的公式，并利用等效原理将求解散射场公式中的体积分简化为面积分的形式，从而降低了求解难度. 同时还推导了两个目标的二次散射场之间的关系. 最后应用给出的公式，求解了两相邻球形目标的复合散射场，对双站散射结果进行了讨论，同时与应用时域积分方程法求得的结果进行了比较. 关键词： 等效原理 互易性定理 电磁散射 相邻圆球     

Study of the reciprocity relations for a nonlinear multipole in inhomogeneous magnetic field

The reciprocity relations for a matrix of nonlinear resistances of a multipole placed in an inhomogeneous magnetic field are obtained based on the material equation of a nonlinear inhomogeneous nonstationary conducting medium in the Landau collision integral approximation. The question about the measured potentials of the multipole terminals in the quasi-stationary mode is discussed. A method for testing the obtained reciprocity relations has been proposed and the experimental data have been presented. It has been shown that the reciprocity relations are valid for a nonlinear multipole within the electric measurement error.     

Non-Local Scattering Kernel and the Hydrodynamic Limit

In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier–Stokes equations.     

Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.     

层状介质上时空展源瞬变电磁响应的计算方法研究

在瞬变电磁法的实际应用中,由于发射回线和发射波形的不规则性而导致其发射源成为时空展源. 展源效应的忽略会造成正反演和数据解释的差错,因此开展展源效应的研究对于瞬变电磁法的实际应用具有重要的意义. 对于空间展源,本文以磁偶极子的响应为基响应,应用有源空间的互易定理和第二类曲线积分,提出了一种可基于发射回线数值坐标求取任意形状发射回线响应的计算方法. 同时对于时间展源,以阶跃波形的响应为基响应,对阶跃响应的特性进行了分析,提出了一种对发射信号进行非均匀采样的高效时间域计算方法,解决了对数采样的基响应与高密度采样的发射波形之间进行常规卷积时所面临的时间与精度之间的矛盾. 通过对层状大地上展源响应的模拟仿真和对比验证显示了本文所提出方法的正确性. 最后本文考察了几种常见时空展源在常规近似前后响应的差别,并给出了相关结论. 关键词： 分层介质 展射电源 互易定理 非均匀采样     

昂色格倒易关系在耐火纤维传热研究中的运用

本文使用昂色格倒易关系对耐火纤维传热过程中的辐射与导热耦合换热进行研究,并通过拟合与数值模拟,总结得出昂色格倒易关系可用于研究多种不同性质基本过程相互耦合的现象。     

昂萨格倒易关系的简要证明

在线性非平衡热力学中,昂萨格倒易关系对其发展起着极为重要的作用.昂萨格倒易关系大大减小了实验分析的困难和工作量,为从实验角度来确定唯象系数提供了可能.本文分别以温度T和体积V以及温度T和粒子数N为自变量证明了昂萨格倒易关系,并探索了熵产生率中力和流的物理本质.