Fluctuations for Kawasaki Dynamics

In this paper Kawasaki dynamics are considered. Lower bounds are obtained for the variance of the occupation time of a site in any dimension and for temperature above critical temperature. These lower bounds are expressed in terms of the density correlation function and hence relate the fluctuations to some phase transition quantities. At critical temperature, under a reasonable assumption of the static structure function, lower bounds for the variance of the occupation time are obtained. These lower bounds are consistent with the supposed value of the critical exponent. This paper also examines the same problem for Glauber dynamics and shows that the phase transition may not be of importance for the behavior of fluctuations.     

Anisotropy Effects in Nucleation for Conservative Dynamics

We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the twodimensional it anisotropic Ising lattice gas at very low temperature. Let LsubsetZ² be a sufficiently large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy U₁<0 in the horizontal direction and U₂<0 in the vertical direction; we assume U₁ges U₂. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e^Db and are annihilated with rate 1, where b is the inverse temperature and D>0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Din (U₁,U₁+U₂) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the it critical droplet/ and the time of its creation in the limit as btoinfty. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern.     

The Spectral Gap of the 2-D Stochastic Ising Model with Mixed Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperatures in an l×l box with boundary conditions which are not purely plus or minus; specifically, we assume the magnitude of the sum of the boundary spins over each interval of length l in the boundary is bounded by l, where <1. We show that for any such boundary condition, when the temperature is sufficiently low (depending on ), the spectral gap decreases exponentially in l.     

The Spectral Gap of the 2-D Stochastic Ising Model with Nearly Single-Spin Boundary Conditions

We establish upper bounds for the spectral gap of the stochastic Ising model at low temperature in an N×N box, with boundary conditions which are plus except for small regions at the corners which are either free or minus. The spectral gap decreases exponentially in the size of the corner regions, when these regions are of size at least of order logN. This means that removing as few as O(logN) plus spins from the corners produces a spectral gap far smaller than the order N ^–2 gap believed to hold under the all-plus boundary condition. Our results are valid at all subcritical temperatures.     

Large deviations for the 2D ising model: A lower bound without cluster expansions

We show that a lower large-deviation bound for the block-spin magnetization in the 2D Ising model can be pushed all the way forward toward its correct Wulff value for all >_c.     

The Spectral Gap of the Ferromagnetic XXZ-Chain

We prove that the spectral gap of the spin- ferromagnetic XXZ-chain with HamiltonianH=–_x S^{(1)}_xS^{(1)}_{x+1}+S^{(2)}_xS^{(2)}_{x+1}+\Delta S^{(3)}_xS^{(3)}_{x+1}, is given by -1 for all 1. This is the gap in the spectrum of the infinite chainin any of its ground states, the translation invariant ones as well asthe kink ground states, which contain an interface between an up and a down region.In particular, this shows that the lowest magnon energy is not affected by the presence of a domain wall. This surprising fact is a consequence of the SU _q (2)quantum group symmetry of the model.     

Constrained variational problem with applications to the Ising model

We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic fieldh, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (–)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of orderB/h withB small enough, while ifB is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical valueB ₀ (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a squeezed Wulff shape. The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.     

Droplet Shapes for a Class of Models in \mathbb{Z}^2 at Zero Temperature

In this work we consider the Wulff construction at zero temperature for a class of Gibbs models and study the shape of the obtained droplets. Considering zero temperature we avoid all difficulties connected with the competition between energy and entropy. It allows us to study a quite wide class of models which provides a variety of shapes. The motivations of the study come from attempts to describe isotropic properties of some models on 2D lattice at zero temperature. The studied models are binary (the spin space is 0,1) with a ferromagnetic behavior such that the potential functions are not equal to zero only for some tiles with size 3×3. In fact, we study herein droplet shapes of a subclass of the ferromagnetic models with potential functions as mentioned above. This subclass of models is defined by a condition called regularity. We call the model classified here as having regular micro-boundaries. Several examples of non-regular models are also presented.     

Surface order large deviations of phase interfaces for the continuum Widom-Rowlinson model in high density limit

We establish a surface order large deviation principle characterising, in the phase coexistence region, the exponential decay rates for the probabilities of macroscopic fluctuations of phase-separating interfaces for the continuum Widom-Rowlinson binary gas, with the thermodynamic and high fugacity limits taken simultaneously. The large deviation rate function is given by an isotropic surface energy functional and hence it attains its minimum for balls which are the most favourable shapes of ‘droplets’ of dominated phase within the ‘ocean’ of dominating phase.     

球形微粒样品室温永久光谱烧孔的动力学过程及多重性研究

利用球粒表面形态共振，实现室温下的永久光谱烧孔，建立理论模型对动力学过程进行分析，据此对实验结果进行拟合，得到有效成孔速率等参数；并对烧孔的多重性进行研究，将这些结果应用于室温频域光信息存贮将有较好的前景。     

Large-density fluctuations for the one-dimensional supercritical contact process

We consider the one-dimensional supercritical contact process. LetT _v be the first time the process reaches a densityq larger than the equilibrium one in the region [1N]. We prove that, starting from equilibrium,T _N /E(T _N ) converges to an exponential random time of mean one. In this way we extend previous results of Lebowitz and Schonmann.     

Improved Bounds on the Spectral Gap Above Frustration-Free Ground States of Quantum Spin Chains

Nachtergaele obtained explicit lower bounds for the spectral gap above many frustration free quantum spin chains by using the martingale method. We present simple improvements to his main bounds which allow one to obtain a sharp lower bound for the spectral gap above the spin-1/2 ferromagnetic XXZ chain. As an illustration of the method, we also calculate a lower bound for the spectral gap of the AKLT model, which is about 1/3 the size of the expected gap.     

低温下JB-9014钝感炸药DSD参数研究

 爆轰冲击波动力学（Detonation Shock Dynamics,DSD）是目前研究爆轰波非理想传播的有效途径。利用DSD的广义几何光学模型,研究了大长径比药柱中爆轰波非理想传播现象,根据-30 ℃下直径为10～30 mm药柱的直径效应实验数据,利用遗传算法确定了低温下JB-9014钝感炸药的DSD参数。由DSD参数计算得到了JB-9014药柱中的定态波形和爆速,计算结果与实验结果符合。     

Global Spectral Gap for Dirichlet-Kac Random Motions

We prove that the global spectral gap, for any Dirichlet-Kac random motion, is equal to the convergence rate of the limit motion.     

On the two-dimensional stochastic Ising model in the phase coexistence region near the critical point

We consider the two-dimensional stochastic Ising model in finite square with free boundary conditions, at inverse temperature >₀ and zero external field. Using duality and recent results of Ioffe on the Wulff construction close to the critical temperature, we extend some of the results obtained by Martinelli in the low-temperature regime to any temperature below the critical one. In particular we show that the gap in the spectrum of the generator of the dynamics goes to zero in the thermodynamic limit as an exponential of the side length of , with a rate constant determined by the surface tension along one of the coordinate axes. We also extend to the same range of temperatures the result due to Shlosman on the equilibrium large deviations of the magnetization with free boundary conditions.     

持久光谱烧孔动力学的理论模型和实验研究

建立了单光子光化烧孔的三能级模型，求解了反映质子转位变构机制的速率方程组，推导了成孔过程的动力学特性，获得了可与实验进行比较的解析解．用时域和频域两种方法测量了ＴＨＰ／ＰＭＭＡ和ＴＭＰ／ＰＭＭＡ薄膜样品光谱烧孔的动力学过程，得到与理论分析一致的规律，并测得了有效成孔速率和成孔时间等参数．这些参数对于评价频域光存贮材料性能有一定意义．     

Damage spreading on the 3–12 lattice with competing Glauber and Kawasaki dynamics

The damage spreading of the Ising model on the 3–12 lattice with competing Glauber and Kawasaki dynamics is studied. The difference between the two kinds of nearest-neighboring spin interactions (interaction between two 12-gons, or interaction between a 12-gon and a triangle) are considered in the Hamiltonian. It is shown that the ratio of the interaction strengthF between the two kinds of interactions plays an important role in determining the critical temperature T_d of phase transition from frozen to chaotic. Two methods are used to introduce the bond dilution on the Ising model on the 3–12 lattice: regular and random. The maximum of the average damage spreading 〈D〉_max can approach values lower than 0.5 in both cases and the reason can be attributed to the ’survivors’ among the spins. We have also, for the first time, presented the phase diagram of the mixed G-K dynamics in the 3–12 lattice which shows what happens when going from pure Glauber to pure Kawasaki     

太阳能选择性吸收涂层高温光谱吸收率的测量方法

太阳能热发电是高效利用太阳能资源的有效途径之一,对缓解能源危机和环境污染具有重要的推动作用和深远的社会意义。选择性吸收涂层是太阳能真空集热管的重要组成部分,是决定太阳能与热能转换效率的关键因素。针对高温状态下太阳能选择性吸收涂层光学性能的表征问题,提出一种适用于高温金属-陶瓷选择性吸收涂层太阳光谱吸收率的测量方法。基于双探测器的傅里叶光谱仪和具有涂层加热功能的积分球,研制了能够防止高温氧化并模拟涂层工作温度的高真空测量装置,实现0.3～2.5 μm、室温-700 ℃太阳光谱吸收率的测量。选取磁控溅射制备的Mo-SiO₂选择性吸收涂层作为测量样品,该样品具有双吸收层的多层膜结构。对涂层样品不同温度下的太阳光谱吸收率进行了测量实验,室温测量值与理论计算值进行了对比分析,结果表明具有较好的一致性,最大偏差仅为2.9%,验证了涂层太阳光谱吸收率测量方法的可行性。高温光谱吸收率测量对涂层参数设计的优化及吸收性能的提高具有重要的指导意义及推动作用。     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

The Asymptotic Behavior of the Ergodic Measure of a Glauber + Kawasaki model

We consider an interacting particle system given by the Glauber + Kawasaki dynamics. It is known that this process has a reaction diffusion equation as hydrodynamic limit. The ergodicity of this process in the presence of a metastable state (double well potential) was recently proved by S. Brassesco et al. In this Letter we prove that, in the limit, as ε → 0, the expected value of each spin converges to the global minimizer of the potential. We also prove decay of correlations of the ergodic measure.AMS Subject Classification (2000). 60K35 (82C22, 82C31)This work was partially supported by CNPq