Phase slip phenomena in superconductors: from ordered to chaotic dynamics

We consider flux penetration to a 2D superconducting cylinder. We show that in the low field limit the kinetics is deterministic. In the strong field limit the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder reduces the level of stochasticity because of the predominance of Kelvin-Helmholtz vortices.     

Phase separation in binary systems with competing internal and external multiplicative noises

We have considered phase separation processes in binary stochastic systems with thermal diffusion and ballistic mixing representing irradiation influence. Introducing fluctuations of thermal flux and an external source of atom relocations due to ballistic diffusion into dynamics of a globally conserved field, we have shown that there are two competing mechanisms of phase transitions type of “order-disorder”: thermally assisted diffusion and irradiation induced atomic exchange. We have studied dynamics of the structure function at early stages of decomposition. In the framework of the mean field theory we have derived the effective Fokker-Planck equation to describe phase separation processes. It was shown that the ordering processes can be controlled by both regular and stochastic parts of external source influence. A reentrant behavior of a mean field order parameter versus the external noise intensity and fluctuations correlation radius is found.     

Modeling microstructure evolution of binary systems subjected to irradiation and mechanical loading

We study a change in mechanical properties of binary systems subjected to irradiation influence described by ballistic flux of atomic mixing having regular and stochastic contributions. By using numerical modeling based on the phase field approach we study dynamics of deformation fields in a previously irradiated system and in the binary system deformed during irradiation. An influence of both deterministic and stochastic components of ballistic flux onto both yield strength and ultimate strength is studied. We have found that degradation of mechanical properties relates to the formation of percolating clusters of shear bands. Considering a hardening coefficient we analyze stages of plastic deformation of both initially irradiated alloy and alloy subjected to sustained irradiation. Stability of binary alloy under mechanical loading in the form of shear strain with a constant rate and cyclic deformation is discussed.     

Dependence of the temperature of stochastically heated electrons on the flux density of pulsed laser radiation on a target

Electron dynamics in the field of focused picosecond multimode laser radiation was considered by numerical methods. It was found that the electron energy during stochastic perturbation of its trajectory can exceed the energy of oscillatory motion in a plane wave by several orders of magnitude. The electron distribution function was studied based on 2D numerical simulation. An analytical expression for the distribution function of relativistic electrons as ideal gas was derived. The distribution function in the radiation flux density range of 10¹⁴–10¹⁷ W/cm² was compared with an analytical expression of the equilibrium distribution; a temperature characteristic for electrons stochastically heated by the laser field was introduced. The dependence of the electron temperature on the radiation flux density was determined.     

随机磁场中的反常扩散效应

本文讨论了随机磁场中反常扩散效应的特征,导出了扩散流及电场随时间变化的公式,指出,趋向于稳态所需的时间远小于粒子约束时间,因而反常扩散基本上是准稳态的形式。此时,存在明显的双极电场,而双极扩散流基本上是离子扩散的量级。 关键词：     

Finite temperature field from stochastic mechanics

Stochastic mechanics of Nelson when generalized to positive temperature for a scalar field, gives rise to a stochastic field which appears to be a hybrid of euclidean and minkowskian field if the usual value of the diffusion parameter is taken. The stochastic process associated with it is a gaussian non-Markov process. The thermal expectations of this stochastic field fails to satisfy the KMS periodic condition. If the diffusion parameter is allowed to continue analytically to a purely imaginary value, the resulting field can be identified with the usual finite temperature quantum field in minkowskian space-time. The relation of this field with that of thermo field dynamics is discussed.     

Flux rope dynamics: experimental study of bouncing and merging

We show experimentally for the first time that two mutually attracting flux ropes may bounce back instead of merging together, leading to a variety of dynamics not expected from a two-dimensional model. Attraction forces due to flux rope currents compete with repulsion from field line bending of in-plane and out-of-plane magnetic fields and elastic plasma compression. Bouncing dynamics occurs if the line-bending force due to an out-of-plane field dominates. Otherwise, the ropes merge. Further reduction in the field line-bending force results in violently erratic magnetic states.     

Noise induced complexity: from subthreshold oscillations to spiking in coupled excitable systems

We study the stochastic dynamics of an ensemble of N globally coupled excitable elements. Each element is modeled by a FitzHugh-Nagumo oscillator and is disturbed by independent Gaussian noise. In simulations of the Langevin dynamics we characterize the collective behavior of the ensemble in terms of its mean field and show that with the increase of noise the mean field displays a transition from a steady equilibrium to global oscillations and then, for sufficiently large noise, back to another equilibrium. In the course of this transition diverse regimes of collective dynamics ranging from periodic subthreshold oscillations to large-amplitude oscillations and chaos are observed. In order to understand the details and mechanisms of these noise-induced dynamics we consider the thermodynamic limit N-->infinity of the ensemble, and derive the cumulant expansion describing temporal evolution of the mean field fluctuations. In Gaussian approximation this allows us to perform the bifurcation analysis; its results are in good qualitative agreement with dynamical scenarios observed in the stochastic simulations of large ensembles.     

随机外磁场作用下Ising自旋体系的随机共振

通过采用数字仿真手段，研究了经平均场处理的Ising自旋体系在弱确定性周期外场和随机外场（噪声场）混合驱动下的动态响应行为.着重考察了不同强度混合驱动外场作用下，Is ing自旋体系的非平衡动态转变所表现出区别于单纯确定性周期场作用下的新特征——随机 共振.选定体系非平衡动态转变的动态序参量Q为表征参量，系统模拟计算了混合驱动外场在多种参数组合下体系的动态响应特征，高场低温下的非连续动态转变和低场高温下的连续动态转变.模拟计算表明在适当混合驱动外场的作用下，Ising自旋体系具有随机共振现象，并诱发形成非 关键词： Ising自旋体系 随机共振 动态相变 对称性     

两种群随机动力系统的信息熵和动力学研究

随机种群动力学模型是研究种群间以及种群与不确定性环境间相互作用的动力学行为的数学模型. 本文从概率密度以及信息熵流、熵产生的演化角度探讨了两种群生态系统的Itô (或Statonovich)意义下随机模型的动力学行为.利用Fokker-Planck方程及其边界条件 和信息熵定义导出信息熵流(平均散度)和熵产生的关系式,并通过数值路径积分法捕 捉到熵流的非线性变化趋势以及信息熵的极值点位置与概率密度的快速迁移和分岔的联系. 应用数值路径积分法计算结果表明Itô (或Statonovich)意义下两种随机模型的概率密度 和信息熵的极值点位置不同但演化趋势一致.     

A Curie-Weiss Model with Dissipation

We consider stochastic dynamics for a spin system with mean field interaction, in which the interaction potential is subject to noisy and dissipative stochastic evolution. We show that, in the thermodynamic limit and at sufficiently low temperature, the magnetization of the system has a time periodic behavior, despite of the fact that no periodic force is applied.     

First passage time on pattern formation in a non-local Fisher population dynamics

We use stochastic dynamics to develop the patterned attractor of a non-local extended system. This is done analytically using the stochastic path perturbation approach scheme, where a theory of perturbation in the small noise parameter is introduced to analyze the random escape of the stochastic field from the unstable state. Emphasis is placed on the specific mode selection that these types of systems exhibit. Concerning the stochastic propagation of the front we have carried out Monte Carlo simulations which coincide with our theoretical predictions.     

SU(3) flux tubes in a model of the stochastic vacuum

We calculate the squared gluon field strengths of a heavyq- $\bar q$ -pair in the model of the stochastic vacuum. We observe that with increasing separation a chromoelectric flux tube is built. The properties of the emerging flux tube are investigated.     

Effect of an alternating field on the relaxation of effect of an alternating field on the relaxation of magnetic flux in a Josephson medium

We establish how trapped magnetic flux depends on the frequency and amplitude of an alternating field and how such a field affects the relaxation rate of the flux. We find that the nature of the flux creep changes in the process and that relaxation of the flux stops after the external field is switched off. We examine the dynamics of flux relaxation in a ring in the approximation in which the current density is assumed homogeneous, for various density dependences of the effective vortex activation energy. The critical current density and the vortex activation energy are obtained as functions of the external field strength. Finally, we explain the observed behavior in terms of the different field profiles emerging in the rings. Zh. éksp. Teor. Fiz. 111, 1047–1056 (March 1997)     

A stochastic posterior Schrödinger equation for counting nondemolition measurement

A stochastic model of the continuous counting nondemolition measurement of photons emitted by an excited atom in a quantum electromagnetic field is given. It is proved that the posterior dynamics of such an atom is described by a new nonlinear stochastic wave equation showing the relaxation of the atom to its ground state due to the photon emission.     

Stochastic resonance between the limiting cycles of precession dynamics

A new type of stochastic resonance that arises between two precession modes under dynamic bistability conditions and is excited by an alternating magnetic field, including a harmonic signal and a white noise, has been studied using a numerical analysis of the uniform magnetization precession in a thin film. The spectrum of the steady-state dynamics of the system at stochastic resonance has been investigated, and its distinctive features have been revealed for the longitudinal and transverse orientations of the additional alternating field.     

Electric field induced by vortex transport in percolation superconductors

The influence of fractal normal phase clusters on the electric field induced by the flow and creep of the magnetic flux in percolation superconductors has been considered. The current–voltage characteristics of such superconductors with allowance for the influence of the fractal dimension of cluster boundaries and the pinning barrier height have been obtained. The vortex dynamics in percolation superconductors with a fractal cluster structure in a viscous flow of the magnetic flux, the Anderson–Kim creep, and the collective flux creep has been analyzed. It has been discovered that the fractality of normal phase clusters reduces the electric field arising in the initial stage of the resistive transition.     

Relaxation to Stationary Nonequilibrium States in Stochastic Ginzburg–Landau Models

We propose an approach to investigate properties of the time relaxation to stationary nonequilibrium states of correlation functions of stochastic Ginzburg–Landau models with noise (temperature of the reservoirs in contact with the system) changing in space. The formalism relates the stochastic expectations to correlation functions of an imaginary time field theory, and it allows us to study the nonlinear dynamics in terms of a field theory given by a perturbation of a Gaussian measure related to the (easier) linear dynamical problem. To show the usefulness of the formalism, we argue that a perturbative analysis within the integral representation is enough to give us the time relaxation rates of the correlations in some situations.     

Landscapes of non-gradient dynamics without detailed balance: stable limit cycles and multiple attractors

Landscape is one of the key notions in literature on biological processes and physics of complex systems with both deterministic and stochastic dynamics. The large deviation theory (LDT) provides a possible mathematical basis for the scientists' intuition. In terms of Freidlin-Wentzell's LDT, we discuss explicitly two issues in singularly perturbed stationary diffusion processes arisen from nonlinear differential equations: (1) For a process whose corresponding ordinary differential equation has a stable limit cycle, the stationary solution exhibits a clear separation of time scales: an exponential terms and an algebraic prefactor. The large deviation rate function attains its minimum zero on the entire stable limit cycle, while the leading term of the prefactor is inversely proportional to the velocity of the non-uniform periodic oscillation on the cycle. (2) For dynamics with multiple stable fixed points and saddles, there is in general a breakdown of detailed balance among the corresponding attractors. Two landscapes, a local and a global, arise in LDT, and a Markov jumping process with cycle flux emerges in the low-noise limit. A local landscape is pertinent to the transition rates between neighboring stable fixed points; and the global landscape defines a nonequilibrium steady state. There would be nondifferentiable points in the latter for a stationary dynamics with cycle flux. LDT serving as the mathematical foundation for emergent landscapes deserves further investigations.