Replica-symmetric solutions of a dilute Ising ferromagnet in a random field

We use the replica method in order to obtain an expression for the variational free energy of an Ising ferromagnet on a Viana-Bray lattice in the presence of random external fields. Introducing a global order parameter, in the replica-symmetric context, the problem is reduced to the analysis of the solutions of a nonlinear integral equation. At zero temperature, and under some restrictions on the form of the random fields, we are able to perform a detailed analysis of stability of the replica-symmetric solutions. In contrast to the behaviour of the Sherrington-Kirkpatrick model for a spin glass in a uniform field, the paramagnetic solution is fully stable in a sufficiently large random field.     

Phase diagram and tricritical behavior of an metamagnet in uniform and random fields

A two-sublattice Ising metamagnet in both uniform and random fields is studied within the mean-field approach based on Bogoliubov’s inequality for the Gibbs free energy. We show that the qualitative features of the phase diagrams are dependent on the parameters of the model and the uniform field values. The tricritical point and reentrant phenomenon can be observed on the phase diagram. The reentrance is due to the competition between uniform and random interactions.     

Error analysis of randomly clipped photo-count correlation estimator

The use of uniform random clipping makes the one-bit correlation function independent of the statistics of the incident field. It has therefore been used in optical spectroscopy to measure the intensity spectrum of non-gaussian fields. This note shows that for a correctly chosen range of clipping, the difference in the error of the estimator and the error expected in a full (multi-bit) correlator decreases inversely as the number of samples. The analysis also applies to one-bit scaling and other methods of uniform random clipping.     

Transport in random correlated fields

A review is given of recent developments in the diffusion properties of particles in the presence of local random fields as well as the conductivity of the analog random resistor network. The effect of long-range ferro- and antiferro-type correlations between the local fields on the diffusion and conductivity properties is considered. A physical realization for such spatial correlations is diffusion on linear polymers in the presence of external uniform bias field. For this case a universal diffusion law was found independent of the fractal dimension of the polymer chain or the Euclidean dimension in which the polymer is embedded. Recent results for diffusion in two dimensions in the presence of a special case of correlated local fields are also reviewed.     

Partially Ordered Models

We provide a formal definition and study the basic properties of partially ordered random fields (PORF). These systems were proposed to model textures in image processing and to represent independence relations between random variables in statistics (in the latter case they are known as Bayesian networks). Our random fields are a generalization of probabilistic cellular automata (PCA) and their theory has features intermediate between that of discrete-time processes and the theory of statistical mechanical lattice fields. Its proper definition is based on the notion of partially ordered specification (POS), in close analogy to the theory of Gibbs measures. This paper contains two types of results. First, we present the basic elements of the general theory of PORFs: basic geometrical issues, definition in terms of conditional probability kernels, extremal decomposition, extremality and triviality, reconstruction starting from single-site kernels, relations between POM and Gibbs fields. Second, we prove three uniqueness criteria that correspond to the criteria known as uniform boundedness, Dobrushin uniqueness and disagreement percolation in the theory of Gibbs measures.     

On the propagation of random electromagnetic fields with position-independent stochastic behavior

A certain kind of vectorial fields with position-independent stochastic behavior is introduced, for which several main features are preserved upon free propagation. For this set of random electromagnetic fields, it is shown that the uniform degree of polarization, the maximum attainable visibility in a Young experiment, and the expansion of the cross-spectral density tensor as the sum of totally-polarized and unpolarized terms are properties that apply for any propagation distance. An elementary example is also shown.     

Driven Rydberg atoms reveal quartic level repulsion

The dynamics of Rydberg states of a hydrogen atom subjected simultaneously to uniform static electric field and two microwave fields with commensurate frequencies is considered in the range of small field amplitudes. In the certain range of the parameters of the system the classical secular motion of the electronic ellipse reveals chaotic behavior. Quantum mechanically, when the fine structure of the atom is taken into account, the energy level statistics obey predictions appropriate for the symplectic Gaussian random matrix ensemble.     

Biological effects of magnetic fields: chronic exposure of the nematode Panagrellus redivivus

The Panagrellus redivivus bioassay, an established monitor of adverse toxic effects of different environments, has been used to study the biological effects of exposure to static and time-varying uniform and gradient magnetic fields, and to time-varying magnetic field gradients superimposed on a static uniform magnetic field of 2.35 Tesla. Temporally stationary magnetic fields have no effect on the fitness of the test animals. Time-varying magnetic fields cause some inhibition of growth and maturation in the test populations. The combination of pulsed magnetic field gradients in a static uniform magnetic field also has a small detrimental effect on the fitness of the test animals.     

The evolution of the nanoscale dissipative structures in a distribution of defects within the isothermally irradiated f.c.c. crystal

A kinetic model for the influence of external noises such as fluctuations of the vacancies’ generation rate and inhomogeneity of irradiated f.c.c. crystal on the formation of nanoscale modulated dissipative structure in a spatial distribution of vacancies is considered. The generation rate of vacancies all over the sites and a density of their dislocation-type sinks are modelled as independent random uniform stationary fields and with certain defined parameters of fluctuation correlations – spatial and temporal ones. Such stochastic fields can induce a spatial redistribution of vacancies that can lead to their density stationary uniform field or stochastic one. By the average value and correlation functions of these fluctuations, the conditions are determined for interacting fluctuations of the vacancies’ density, under which this homogeneous random field becomes unstable in relation to the stochastic field with a spatially periodic mean distribution of vacancies’ density. For instance, with f.c.c. nickel as a model of the irradiated functional material, the temperature dependence of spatial period d(T) of the modulated dissipative structure of vacancies’ subsystem in f.c.c. crystal is numerically forecasted and analysed, taking into account the total (‘electrochemical’?+?‘strain-induced’) interaction between vacancies. Such d(T)-dependence is also determined by the kinetic characteristics of vacancies’ redistribution.     

One-dimensional numerical simulations of random sound impulses

Abstract

We perform one-dimensional numerical simulations of small-amplitude acoustic pulses in space- and time-dependent random mass density and time-dependent velocity fields. Numerical results reveal that: (a) random fields affect the speeds, amplitudes and, consequently, shapes of sound pulses; (b) for weak random fields and short propagation times the numerical data converge with the analytical results of the mean field theory which says that a space-dependent (time-dependent) random field leads to wave attenuation (amplification) and all random fields speed up sound pulses; (c) for sufficiently strong random fields and long propagation times numerical simulations reveal pulse splitting into smaller components, parts of which propagate much slower than a wave pulse in a non-random medium. These slow waves build an initial stage of a wave localization phenomenon. However, this effect can be very weak in a real three-dimensional medium.     

Can Extra Updates Delay Mixing?

We consider Glauber dynamics (starting from an extremal configuration) in a monotone spin system, and show that interjecting extra updates cannot increase the expected Hamming distance or the total variation distance to the stationary distribution. We deduce that for monotone Markov random fields, when block dynamics contracts a Hamming metric, single-site dynamics mixes in O(n log n) steps on an n-vertex graph. In particular, our result completes work of Kenyon, Mossel and Peres concerning Glauber dynamics for the Ising model on trees. Our approach also shows that on bipartite graphs, alternating updates systematically between odd and even vertices cannot improve the mixing time by more than a factor of log n compared to updates at uniform random locations on an n-vertex graph. Our result is especially effective in comparing block and single-site dynamics; it has already been used in works of Martinelli, Toninelli, Sinclair, Mossel, Sly, Ding, Lubetzky, and Peres in various combinations.     

Tricritical Points and Reentry in the Quantum Hopfield Neural-Network Model

We examine a quantum Hopfield neural-network model in the presence of trimodal random transverse fields and random neuronal thresholds within the method of statistical physics. We use the Trotter decomposition to map the problem into an equivalent classical random Hopfield-type Ising model and obtain phase transitions between the ferromagnetic retrieval and the paramagnetic phases. The influence of competition between the diluted random transverse fields and the diluted random thresholds on the system is discussed, and some interesting results such as tricritical points and reentrance are analyzed.     

Low field microwave absorption and magnetic flux quantization in granular Rb3C60: Observation of nonperiodic sharp line microwave absorption

The low field microwave absorption (LFMA) of granular samples of superconducting Rb₃C₆₀ has been studied as a function of the microwave power, magnetic field modulation amplitude and temperature at dc magnetic fields less than 0.5 G. Nonperiodic sharp lines are observed for the first time in these new alkali-metal doped fullerenes. An interpretation is advanced based on a spin-glass model of a set of superconducting current loops with random orientations but uniform areas.     

A universal algorithm to generate pseudo-random numbers based on uniform mapping as homeomorphism

A specific uniform map is constructed as a homeomorphism mapping chaotic time series into [0,1] to obtain sequences of standard uniform distribution. With the uniform map, a chaotic orbit and a sequence orbit obtained are topologically equivalent to each other so the map can preserve the most dynamic properties of chaotic systems such as permutation entropy. Based on the uniform map, a universal algorithm to generate pseudo random numbers is proposed and the pseudo random series is tested to follow the standard 0-1 random distribution both theoretically and experimentally. The algorithm is not complex, which does not impose high requirement on computer hard ware and thus computation speed is fast. The method not only extends the parameter spaces but also avoids the drawback of small function space caused by constraints on chaotic maps used to generate pseudo random numbers. The algorithm can be applied to any chaotic system and can produce pseudo random sequence of high quality, thus can be a good universal pseudo random number generator.     

均匀外场中扩散控制聚集集团标度性质的实验

本文采用无分岔扩散控制聚集(DLA)模型,利用计算机模拟均匀外场中微小颗粒的不可逆生长过程,发现均匀外场的存在将改变生长集团的标度性质。对在均匀外场中生长的DLA,集团的豪斯道夫维数D与均匀外场F之间存在函数关系:D=2.50F^0.37exp(-1.08F)+1。 关键词：     

对均匀的数学描述及其与混沌的关系

基于独占球的概念定义的瞬时混沌度和k步混沌强度是混沌轨道的稳定特征,应用独占球的概念定义了均匀度,它对均匀性的描述与人对均匀的理解非常符合.被含均匀度是一个过渡概念,它与均匀度非常相似,但有更好的数学性质,对于随机轨道,被含均匀度统计收敛于1/V_n（1）（V_n（1）是n维欧氏空间的单位球体积）,而当轨道上的点充分多时,均匀度与被含均匀度近似相等.只要适当选择包含动力系统吸引盆的多 关键词： 独占球 均匀度 混沌 瞬时混沌强度     

Representations of Canonical Commutation Relations Describing Infinite Coherent States

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.     

Aspects of magnetic disorder

A brief review is given of the effects that quenched, magnetic disorder have on the magnetic properties of systems with short-range interactions. Of primary interest are random exchange, random anisotropy and random fields. Recent theoretical and experimental studies have begun to illuminate the unusual critical behavior that is seen in randomly diluted antiferromagnets in the presence of a uniform field, which is the most direct manner by which the random field problem may be approached. Considerable uncertainty still exists as to what is the lower critical dimensionalityd ₁ and the effective dimensionality ¯d ford-dimension Ising systems in the presence of a random field. This whole area appears to be one in which further insight might be gained through the application of microscopic probes such as NMR, Mössbauer Effect andSR.