Stark resonances in disordered systems

We study further the metastable behavior of Metropolis dynamics for the two-dimensional nearest neighbor ferromagnetic Ising model, with positive and small external field, in the limit as the temperature vanishes (see [NS]). We focus on the typical features of the escape (nucleation) from the (metastable) configuration with all spins –1, to the (stable) configuration with all spins +1. Using the reversibility of the process as the main tool, we prove (for the discrete time version of the model) that the first step of a typical escaping path is the time reverse of a typical time evolution of a shrinking subcritical rectangular droplet, which is one slice smaller than a critical droplet. This subcritical droplet then evolves in a time of order 1 to a critical droplet, which finally grows with features described in [NS].Work partially supported by the Brazilian CNPq and by the American NSF, under grant DMS91-00725     

AlCuFe quasicrystals: Local electronic properties of these new industrial materials

We present room temperature ⁵⁷Fe Mössbauer centre (isomer) shift and electric field gradient (EFG) results in the Al_100-x-yCu_xFe_y icosahedral-quasicrystalline (i-) and crystalline phases. We have investigated the local electronic properties and atomic order along the existence domains of the quasicrystalline and approximant phases given by two close-lying parallel lines in the concentration diagram: the I-line, where the quasicrystal is stable, and the A-line, where the rhombohedral approximant is stable, and other high-order approximants (orthorhombic and pentagonal) as well as the quasicrystal phase are metastable. We have also studied a series of intermediate concentrations situated between the I- and A-lines retained in the metastable i-phase by quenching. It is found that the centre shift and EFG are linearly correlated to each other over the range of compositions and structures for both the I- and A-lines as well as the intermediate samples. This correlation results from systematic changes in the orbital occupations on Fe atoms with composition. We have investigated as well the new low-order cubic approximant phase containing Si. The results for this phase fall near to but not on the correlation line indicating small changes in the atomic binding as compared to the i- and high order approximant phases. In addition, we have studied several non-approximant phases which lie close to these phases in composition. The results for the non-approximant structures do not fall near the correlation line, indicating very different atomic binding.     

Calculation of minor hysteresis loops under metastable to stable transformations in vortex matter

We present a model in which metastable supercooled phase and stable equilibrium phase of vortex matter coexist in different regions of a sample. Minor hysteresis loops are calculated with the simple assumption of the two phases of vortex matter having field-independent critical current densities. We use our earlier published ideas that the free energy barrier separating the metastable and stable phases reduces as the magnetic induction moves farther from the first order phase transition line, and that metastable to stable transformations occur in local regions of the sample when the local energy dissipation exceeds a critical value. Previously reported anomalous features in minor hysteresis loops are reproduced, and calculated field profiles are presented.     

Existence of excited states for a nonlinear Dirac field

We prove the existence of infinitely many stationary states for the following nonlinear Dirac equation $$i\gamma ^\mu \partial _\mu \psi - m\psi + (\bar \psi \psi )\psi = 0.$$ Seeking for eigenfunctions splitted in spherical coordinates leads us to analyze a nonautonomous dynamical system inR ². The number of eigenfunctions is given by the number of intersections of the stable manifold of the origin with the curve of admissible datum. This proves the existence of infinitely many stationary states, ordered by the number of nodes of each component.     

Critical droplets and metastability for a Glauber dynamics at very low temperatures

We consider the metastable behavior in the so-called pathwise approach of a ferromagnetic spin system with a Glauber dynamics in a finite two dimensional torus under a positive magnetic field in the limit as the temperature goes to zero. First we consider the evolution starting from a single rectangular droplet of spins +1 in a sea of spins −1. We show that small droplets are likely to disappear while large droplets are likely to grow; the threshold between the two cases being sharply defined and depending only on the external field. This result is used to prove that starting from the configuration with all spins down (−1) the pattern of evolution leading to the more stable configuration with all spins up (+1) approaches, as the temperature vanishes, a metastable behavior: the system stays close to −1 for an unpredictable time until a critical square droplet of a precise size is eventually formed and nucleates the decay to +1 in a relatively short time. The asymptotic magnitude of the total decay time is shown to be related to the height of an energy barrier, as expected from heuristic and mean field studies of metastability. Partially supported by CNPq. Part of this work was done while RHS was visiting Rome, supported by an agreement between CNPq and CNR     

Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.     

Metastable superpositions of ortho- and para-Helium states

We analyze superpositions of ortho- and para-Helium states, considering the possible existence of stationary and metastable states in the system. In particular, the metastable superposition of 1s2s ortho- and para-states seems to be accessible to experimental scrutiny.     

Stochastic Theory of Nucleation in Nonequilibrium Bistable Reaction Systems

Nucleation is one of the fundamental types of forming stable dissipative nonequilibrium structures in metastable initial states. The nucleation process of a bistable chemical reaction system is investigated. First a microdroplet with radius R₀ of the new state imbedded in the parent one is formed by a local particle number fluctuation. The radius of the microdroplet R(t) fluctuates due to the interference of reaction and diffusion. If R(t) considerably exceeds a critical value R_k the droplet starts to grow deterministically. The mean nucleation time of one droplet in weakly supersaturated systems is calculated using the concept of the mean first passage time.     

Compactification and supersymmetry in d = 11 supergravity

We examine the conditions under which the ground state of d = 11 supergravity can be supersymmetric and be of the form M⁴ ? B⁷ with M⁴ Minkowski spacetime and B⁷ a compact seven-dimensional manifold. Since we have in mind a background that renders the effective action stationary we make no use of the classical field equations. We find that the requirement that the four-space be flat is very restrictive. It requires all components of the background four-index field to vanish and the compact manifold to be Ricci-flat and hence to have at most the abelian symmetries associated with tori.     

Metastability and superfluid fraction of the A-like and B phases of <Superscript>3</Superscript>He in aerogel in zero magnetic field

We report the low-frequency sound measurements of the metastable A-like (A*) phase of superfluid ³He confined within a 98% open aerogel matrix in zero magnetic field. The second soundlike (slow) mode provides an accurate determination of the superfluid fraction of (and the transition between) the A* and B phases. The A* and B phases exhibit stable coexistence in the presence of disorder, the ratio of their superfluid fractions (ρ _a ^A* /ρ _s ^B ) is much smaller than that of the bulk A and B phases, and argues that the A* and bulk A phases are distinct.     

Sharp Asymptotics for Stochastic Dynamics with Parallel Updating Rule

In this paper we study the metastability problem for a stochastic dynamics with a parallel updating rule; in particular we consider a finite volume Probabilistic Cellular Automaton (PCA) in a small external field at low temperature regime. We are interested in the nucleation of the system, i.e., the typical excursion from the metastable phase (the configuration with all minuses) to the stable phase (the configuration with all pluses), triggered by the formation of a critical droplet. The main result of the paper is the sharp estimate of the nucleation time: we show that the nucleation time divided by its average converges to an exponential random variable and that the rate of the exponential random variable is an exponential function of the inverse temperature β times a prefactor that does not scale with β. Our approach combines geometric and potential theoretic arguments.     

LaFe11.4Al1.6中铁磁相与反铁磁相的双相共存

通过磁场下热磁曲线的测量，在LaFe114Al16化合物中发现了一个在一定温区内随温度稳定的铁磁相和反铁磁相的共存亚稳态.确定了这个亚稳态能够存在的磁场和温度范围，从而使LaFe114Al16化合物的磁相图更加完善.这个亚稳态的温度稳定性能够很好地解释磁性转变的临界场随温度的变化行为.这个双相共存亚稳态的存在，与LaFe114Al16中的磁性交换作用及晶格畸变所产生的边界相的稳定性有关. 关键词： 共存相 亚稳态 晶格畸变     

亚稳相的高压暴露

 很久以前,便有人指出,气态冷凝成固态时,要连续经历液相及各种高温相,才达到平衡结晶相。但是,液态及高温相往往需靠很大的冷却速度才能冻结下来,这在当时对绝大多数合金,是不可能的。近些年,随着超急冷等技术的进步,关于非晶等亚稳相得研究十分活跃。当超过一定临界冷却速度时,液态合金可固化为非晶态。虽然,亚稳结晶相较非晶应更容易冻结,但是,由于产生各种亚稳相所需的过冷条件各不相同,以及对冷却速度的选择不能是任意的,因此有时它们较非晶还难于形成。与液相凝固过程相似,非晶合金的晶化也服从构型最小重排原理,即在晶化完成之前,存在某些亚稳相变态阶段。但是,限于热力学上的不稳定性及动力学因素,在常压下这些亚稳相同样是难以发现的。作者根据对多种合金系的研究,提出高压暴露亚稳相的设想,并利用非晶等亚稳相的高压变态过程,将进行液态急冷时的速度控制方式,改为便于掌握的高压退火方式,来获得新亚稳相。本文对压力暴露亚稳相的原理和实践,加以论述。     

Study of the polymorphism of binary solutions of molecular substances in microsamples

Previous studies have shown that certain molecular substances taken in microsamples (droplets of about 1 μm³ in volume dispersed within an emulsion) crystallize into metastable crystalline phases. These compounds are studied in solution with benzene which does not show metastable polymorphism. The binaries benzene-1-2 dichlorobenzene, benzene-chloroform and benzene-nitrobenzene in emulsion are investigated by D.S.C. techniques. Metastable phases appear, too, and it is possible to draw metastable liquidus and locate metastable eutectics in the phase diagrams. In benzene-chloroform solution at least one new metastable phase is detected. In the benzene-nitrobenzene binary a metastable phase is detected, although neither benzene nor nitrobenzene show a metastable crystalline phase when they are pure.     

Self-organization of a critical state on complex networks

The critical dynamics of a two-threshold system with the law of conservation of the basic quantity z and in the absence of sink on a scale-free network has been studied. It has been shown that the critical state that is a set of metastable states appears in such a system. The structure of the metastable states is a set of stable clusters of nodes at which the z values are close to the positive and negative threshold values. Avalanches transforming the system from one metastable state to another state appear in the system. The absence of sink is effectively replaced by the annihilation process. The statistics of avalanches in such a system has been analyzed. It has been shown that the self-organized critical state can appear in the system.     

Crystalline thiophene. II: a comprehensive study of stable and metastable phases by means of heat capacity,thermally stimulated currents and raman spectroscopy measurements

This calorimetric study of crystalline thiophene between 77 and 250 K reveals the existence of four phase transitions at 174.50, 170.49, 136.8 and 111.26 K, respectively. The transition II-III (170.49 K) is easily avoided during cooling, leading to metastable phases, which, in turn, exhibit their own phase transitions.These findings explain previously confused observations. The existence of stable and metastable phases was confirmed by thermally stimulated current measurements. Intermolecular Raman spectra were observed between 10 and 300 K and assigned to the observed phases. Some predictions are made concerning the low-temperature behaviour of thiophene. Tentative rules are proposed to number metastable phases relative to stable ones.     

Critical droplets near coexistence of wet and nonwet surface states

In first-order wetting transitions the decay of metastable states starts with a nucleation process on the wall of the system. For a planar wall the critical droplet has cylindrical symmetry and therefore should be described by two different critical lengths. We discuss these quantities and also the excess free energy of the critical droplet as functions of the spreading coefficient near coexistence of the wet and the nonwet state of the wall.     

Thermodynamically stable pickering emulsions

We show that under appropriate conditions, mixtures of oil, water, and nanoparticles form thermodynamically stable oil-in-water emulsions with monodisperse droplet diameters in the range of 30-150 nm. This observation challenges current wisdom that so-called Pickering emulsions are at most metastable and points to a new class of mesoscopic equilibrium structures. Thermodynamic stability is demonstrated by the spontaneous evolution of binary droplet mixtures towards one intermediate size distribution. Equilibrium interfacial curvature due to an asymmetric charge distribution induced by adsorbed colloids explains the growth of emulsion droplets upon salt addition. Moreover, the existence of a minimal radius of curvature with a concomitant expulsion of excess oil is in close analogy with microemulsions.