Transient bimodality in interacting particle systems

We consider a system of spins which have values ±1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flipGlauber process, the other aKawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor ^–2, then, in the limit 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. We choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. We assume further that for each the system is in a finite interval ofZ with ^–1 sites and periodic boundary conditions. We specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. We prove that at times of the order ^–1/2 propagation of chaos does not hold any more and, in the limit as 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale ^–1/2) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo.     

Van der waals limit and phase separation in a particle model with kawasaki dynamics

A one-dimensional interacting particle system with a stochastic dynamics is studied in the local mean field limit, extending the results of Lebowitz, Orlandi, and Presutti to processes which satisfy detailed balance (with respect to Gibbs measures). The behavior of the system below the critical temperature and inside the unstable (spinodal) region is then investigated by means of computer simulations. The experiments clearly indicate the presence of phase separation and confirm the validity of some conjectures on the dynamics of the spinodal decomposition.     

Monte Carlo studies of a driven lattice gas. I. Growth and asymmetry during phase segregation

We investigate the effects of an external field on the kinetics of phase segregation in systems with conservative diffusive dynamics. We find that, in contrast to the situation without a field, there are now qualitative differences between the results of microscopic simulations of a 2D lattice model with biased Kawasaki exchanges and those obtained from various modifications of the macroscopic Cahn-Hilliard equation (mCH). While both microscopic simulations and numerical solutions of MCH yield triangular domains, we find that in the former the triangles mainly pointopposite to the field, while in the latter and in new calculations with the mCH they pointalong the field. On the other hand, the rate of growth of the clusters and their final state, bands parallel to the field, are similar. This issue and the question of the mesoscopic behavior of cell dynamical systems is discussed but not resolved.     

Decay to equilibrium in random spin systems on a lattice. II

We study the continuous spin systems on ad3-dimensional lattice with random ferromagnetic interactions of finite range. We show that, if the temperature is sufficiently high and the probability of interaction to be large is small enough, the almost sure decay to equilibrium has a subexponential upper bound.     

Phase separation dynamics in driven diffusive systems

We study phase separation dynamics in a driven diffusive system. Our simulations are based on the Cahn-Hilliard equation with an additional flux term due to an external field. We study the dynamical scaling parallel and perpendicular to the field. A crossover is observed from isotropic domains at early times to extremely anisotropic domains at later times. We find that the inverse interfacial density (an isotropic measure of the domain size) increases ast , with =1/3, from early times independent of the field strength, even though we do not observe dynamical scaling during these times. Our results indicate that a growth exponent =1/3 may be more universal than previously expected. We analyze the dynamics in terms of surface driven instabilities and one-dimensional solitary waves.     

Order and disorder lines in systems with competing interactions: I. Quantum spins atT=0

In the parameter space of systems with competing interactions there are specific trajectories called order (disorder) lines. Along these trajectories the competition between the different interactions effectively reduces the dimensionality of the system and the model can be exactly solved. It is shown that the order (disorder) trajectories end up at a multicritical point. The method of Peschel and Emery is used to determine the (anisotropic) critical behavior of the spin-spin correlation functions near the multicritical point. The quantum spin systems discussed here include theXYZ chain in a field, the straggeredXYZ chain in a field, and a Hamiltonian version of a three-dimensional Ising model with biaxial competing interactions.On leave from and address after September 1, 1982: Institute for Theoretical Physics, Eötvös University, Puskin U. 5-7, 1088 Budapest, Hungary.     

Energy transport in boundary driven quantum spin systems: One-way street phenomenon in models with long range interactions

We address the investigation of non trivial properties of the energy current in boundary driven XXZ quantum spin models. In specific, we focus on the occurrence of the one-way street phenomenon in asymmetrical chains, a phenomenon stronger than rectification, which establishes the existence of a unique way for the energy current in the absence of external magnetic field, that is, the magnitude and direction of the energy flow does not change as we invert the baths at the boundaries. For general target polarizations at the boundaries, we show that such a phenomenon holds in the presence of long range interactions, ingredient which increases the flow and the rectification in chains of classical oscillators, and so, of interest in the study of manipulation and control of the energy flow.     

Hydrodynamics and Platoon Formation for a Totally Asymmetric Exclusion Model with Particlewise Disorder

We consider a one-dimensional totally asymmetric exclusion model with quenched random jump rates associated with the particles, and an equivalent interface growth process on the square lattice. We obtain rigorous limit theorems for the shape of the interface, the motion of a tagged particle, and the macroscopic density profile on the hydrodynamic scale. The theorems are valid under almost every realization of the disordered rates. Under suitable conditions on the distribution of jump rates the model displays a disorder-dominated low-density phase where spatial inhomogeneities develop below the hydrodynamic resolution. The macroscopic signature of the phase transition is a density discontinuity at the front of the rarefaction wave moving out of an initial step-function profile. Numerical simulations of the density fluctuations ahead of the front suggest slow convergence to the predictions of a deterministic particle model on the real line, which contains only random velocities but no temporal noise.     

Phase transitions in small systems: Microcanonical vs. canonical ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.     

Phase transitions in electron systems with short-range pairing interactions: Ground state

We propose a real-space, tight-binding model of electrons with short-range pairing interactions. The model involves a competition between the ordinary single particle hoppingt and an attractive interactionV between the singlet electronic pairs formed on neighboring lattice sites. The Hamiltonian effectively describes a mechanism for pair formation. We study the ground-state properties of its onedimensional version using numerically exact finite chain calculations for up toN= 10 sites. The ground-state wave functions, the energy spectrum, and various ground-state correlation functions are calculated with the help of an exactly equivalent system of two coupledS=1/2 spin chains. The results indicate the existence of a transition between the band and the localized pairs situation. The transition takes place forV/t= 1.4–0.1 and appears to be of essential singularity type. Comparison with other models used for pairing phenomena, like the negativeU-Hubbard model is made.     

基于量子并行粒子群优化算法的分数阶混沌系统参数估计

分数阶混沌系统参数估计的本质是多维参数优化问题, 其对于实现分数阶混沌控制与同步至关重要. 提出一种基于量子并行特性的粒子群优化新算法, 用于解决分数阶混沌的系统参数估计问题. 利用量子计算的并行特性, 设计出了一种新的量子编码, 使每代运算的可计算次数呈指数增加. 在此基础上, 构建了由量子当前旋转角、个体最优旋转角和全局最优旋转角共同组成的粒子演化方程, 以约束粒子在量子空间中的运动行为, 使算法的搜索能力得到了较大提高. 以分数阶Lorenz混沌系统和分数阶Chen混沌系统的参数估计为例, 进行了未知参数估计的数值仿真, 结果显示本算法具有良好的有效性、鲁棒性和通用性.     

Collective effects for long bunches in dual harmonic RF systems

The storage of long bunches for large time intervals needs flattened stationary buckets with a large bucket height.Collective effects from the space charge and resistive impedance are studied by looking at the incoherent particle motion for the matched and mismatched bunches.Increasing the RF amplitude with particle number provides r.m.s wise matching for modest intensities.The incoherent motion of large amplitude particles depends on the details of the RF system.The resulting debunching process is a combination of the too small full RF acceptance together with the mismatch,enhanced by the collective effects.Irregular single particle motion is not associated with the coherent dipole instability.For the stationary phase space distribution of the Hofmann-Pedersen approach and for the dual harmonic RF system,stability limits are presented,which are too low if using realistic input distributions.For single and dual harmonic RF system with d＝0.31,the tracking results are shown for intensities,by a factor of 3 above the threshold values.Small resistive impedances lead to coherent oscillations around the equilibrium phase value,as energy loss by resistive impedance is compensated by the energy gain of the RF system.     

Phase transitions in two-dimensional uniformly frustratedXY models. I. Antiferromagnetic model on a triangular lattice

A most popular model in the family of two-dimensional uniformly-frustratedXY models is the antiferromagnetic model on a triangular lattice [AFXY(t) model]. Its ground state is both continuously and twofold discretely degenerated. Different phase transitions possible in such systems are investigated. Relevant topological excitations are analyzed and a new class of such (vortices with a fractional number of circulation quanta) is discovered. Their role in determining the properties of the system proves itself essential. The characteristics of phase transitions related to breaking of discrete and continuous symmetries change. The phase diagram of the generalized AFXY(t) model is constructed. The results obtained are rederived in the representation of the Coulomb gas with half-integer charges, equivalent to the AFXY(t) model with the Berezinskii-Villain interaction.