算法对混沌体系逃逸率的影响

以Hénon-Heiles体系为例，研究算法对混沌体系运动轨道和逃逸率计算结果的影响.比较了新发现的四阶辛算法和一种非辛的高阶算法得到的结果.发现两种算法给出的轨迹之间的距离随时间增大，增加的速度可以作为体系相空间混沌的度量.通过跟踪大数量的粒子轨迹，提取出了逃逸率随体系能量的变化.发现由两种算法得到的逃逸率相互符合得很好. 关键词： 逃逸率 Hénon-Heiles体系 辛算法     

Dynamics of activated escape and its observation in a semiconductor laser

We report a direct experimental observation and provide a theory of the distribution of trajectories along which a fluctuating system moves over a potential barrier in escape from a metastable state. The experimental results are obtained for a semiconductor laser with optical feedback. The distribution of paths displays a distinct peak, which shows how the escaping system is most likely to move. We argue that the specific features of this distribution may give an insight into the nature of dropout events in lasers.     

Escape of Particles from an Open Square-Shaped Cavity

The escape of particles in an open square-shaped cavity has been examined. We consider a family of trajectories launched from the left bottom lead of the square cavity and escaped from the right boundary. For each escaping trajectories, we record the propagation time and the detector position. We find that the escape time graph exhibits a regular sawtooth structure. For a set of detector points, we search for the classical trajectories from the source point to the detector points. Then we use semiclassical theory to construct the wave function at different given points. The calculation results suggest that the escape probability density depends on the detector position and the momentum of the particle sensitively. The Fourier transform of the semiclassical wave function gives the path length spectrum. Each peak in the path length spectrum corresponds to the length of one escape trajectory of the particle. We hope that our results will be useful in understanding the escape and transport process of particles inside a microcavity.     

Enhanced diffusion due to active swimmers at a solid surface

We consider two systems of active swimmers moving close to a solid surface, one being a living population of wild-type E.?coli and the other being an assembly of self-propelled Au-Pt rods. In both situations, we have identified two different types of motion at the surface and evaluated the fraction of the population that displayed ballistic trajectories (active swimmers) with respect to those showing randomlike behavior. We studied the effect of this complex swimming activity on the diffusivity of passive tracers also present at the surface. We found that the tracer diffusivity is enhanced with respect to standard Brownian motion and increases linearly with the activity of the fluid, defined as the product of the fraction of active swimmers and their mean velocity. This result can be understood in terms of series of elementary encounters between the active swimmers and the tracers.     

Photoionization Microscopy of Rydberg Hydrogen Atom in a Generalized van der Waals Potential

The ionization dynamics of a Rydberg hydrogen atom in a generalized van der Waals potential is studied using a semiclassical analysis of photoionization microscopy. Interference patterns of the 2-D radial probability density of the electrons escaping from a photoionization process have been calculated to simulate the patterns recorded on a position-sensitive detector. The added contributions from different ionization trajectories from the atom to the detector generate the interference pattern. The interference pattern is sensitive to one of the parameters governing the electron motion in the generalized van der Waals potential. The photoionization microscopy pattern can therefore be controlled by changes in the external potential.     

Phase probability density in subensembles of a quantum mode of a one-atom maser

The method of periodic trajectories is applied to the analysis of the phase states of a one-atom maser mode, information on which can be obtained from a series of consequent indirect phase-sensitive quantum measurements of atoms leaving the cavity. Such information allows one to study in detail the evolution of a maser mode in a stationary state. The evolution pattern is represented as a random sequence of subensembles in which the mode exists during different time intervals. An approximate stochastic recurrence relation is obtained, which allows us, using the Monte Carlo method, to generate a sequence of relative frequencies of detection of the states of a chosen basis in escaping atoms. Formulas for the phase probability density for subensembles of the mode are derived. These formulas are obtained using as initial data the average relative frequencies measured by an experimenter in a region of a stable trajectory.     

Critical behaviour in deterministic motion in a random environment

A numerical study of deterministic motion in a random environment in two dimensions is performed. All trajectories are localised except at two isolated points in the parameter space. The distribution of trajectory lengths shows “critical” behaviour as those points are approached. Contact with an analytic estimate, based on analogy with gelation theory, is made in one region of the parameter space. The spatial extent of the trajectories scales with arc length as if they were ideal random walks, surprisingly.     

Directed transport of two interacting particles in a washboard potential

We study the conservative and deterministic dynamics of two nonlinearly interacting particles evolving in a one-dimensional spatially periodic washboard potential. A weak tilt of the washboard potential is applied biasing one direction for particle transport. However, the tilt vanishes asymptotically in the direction of bias. Moreover, the total energy content is not enough for both particles to be able to escape simultaneously from an initial potential well; to achieve transport the coupled particles need to interact cooperatively. For low coupling strength the two particles remain trapped inside the starting potential well permanently. For increased coupling strength there exists a regime in which one of the particles transfers the majority of its energy to the other one, as a consequence of which the latter escapes from the potential well and the bond between them breaks. Finally, for suitably large couplings, coordinated energy exchange between the particles allows them to achieve escapes — one particle followed by the other — from consecutive potential wells resulting in directed collective motion. The key mechanism of transport rectification is based on the asymptotically vanishing tilt causing a symmetry breaking of the non-chaotic fraction of the dynamics in the mixed phase space. That is, after a chaotic transient, only at one of the boundaries of the chaotic layer do resonance islands appear. The settling of trajectories in the ballistic channels associated with transporting islands provides long-range directed transport dynamics of the escaping dimer.     

Metrics for ergodicity and design of ergodic dynamics for multi-agent systems

In this paper we propose a metric that quantifies how far trajectories are from being ergodic with respect to a given probability measure. This metric is based on comparing the fraction of time spent by the trajectories in spherical sets to the measure of the spherical sets. This metric is shown to be equivalent to a metric obtained as a distance between a certain delta-like distribution on the trajectories and the desired probability distribution. Using this metric, we formulate centralized feedback control laws for multi-agent systems so that agents trajectories sample a given probability distribution as uniformly as possible. The feedback controls we derive are essentially model predictive controls in the limit as the receding horizon goes to zero and the agents move with constant speed or constant forcing (in the case of second-order dynamics). We numerically analyze the closed-loop dynamics of the multi-agents systems in various scenarios. The algorithm presented in this paper for the design of ergodic dynamics will be referred to as Spectral Multiscale Coverage (SMC).     

Bound-bound state quantum wave packet dynamics in the intermediate coupling range: the A1Sigma+u (0+u) and b3IIu (0+u) system in Rb2

The real-time quantum dynamics of a wave packet confined to two coupled bound states at intermediate interaction strength is probed by experiment and calculations on the A1Sigma(+)(u) approximately b (3)II(u) system in Rb2 molecules. The general dynamics consists of rapid spreading out over the whole phase space. Particular conditions exist, however, under which the initial wave packet motion separates into two mesobatic trajectories with distinct frequencies. These diabatic or adiabatic hybrid trajectories are analogous to those responsible for longevity resonances in bound-unbound systems.     

Coefficient de transfert, à l'interface de vaporisation,d'une boucle fluide diphasique à pompage thermocapillaire

Heat transfer coefficient at vaporisation interface of a two phase capillary loop. In this article, we present the results of heat transfer coefficient measurements at the vaporisation interface of a capillary pumped two-phase loop for two different types of evaporators and various powers. High contact between the evaporator wall and the porous wick, which induces capillary pumping, prevents vapor from escaping and being forced back into the wick and inhibits the device starting up. First, the surface state of the evaporator wall, then the minimum distance between wall and porous wick necessary to optimize operating conditions have been established.     

Detecting coherent structures using braids

The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of oil spills. Existing methods detect Lagrangian coherent structures, which are barriers to transport, by examining the stretching field as given by finite-time Lyapunov exponents. These methods are very effective when the velocity field is well-determined, but in many applications only a small number of flow trajectories are known, for example when dealing with oceanic float data. We introduce a topological method for detecting invariant regions based on a small set of trajectories. In this method, we regard the two-dimensional trajectory data as a braid in three dimensions, with time being the third coordinate. Invariant regions then correspond to trajectories that travel together and do not entangle other trajectories. We detect these regions by examining the growth of hypothetical loops surrounding sets of trajectories, and searching for loops that show negligible growth.     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式。我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹。对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置。结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构。随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端。对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式。研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关。为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱。路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度。本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程可以提供一定的参考价值。     

粒子在二维开放型四分之一圆形微腔中的逃逸研究

利用半经典理论对粒子在开放型四分之一圆形微腔中的逃逸过程进行了研究,推导出了逃逸几率密度的计算公式.我们研究了一簇从四分之一圆形微腔的左下方的入口出射、并从该微腔右边界逃逸的粒子轨迹.对于粒子的每一条逃逸轨迹,记录下它的传播时间和逃逸的位置.结果发现逃逸时间图随着逃逸点的位置的变化曲线呈现出振荡结构.随着碰撞次数的增加,逃逸点的位置越靠近该腔的右顶端.对一系列的探测点,找到从源点出发到达探测点的轨迹,然后应用半经典理论来构造波函数,进而给出逃逸几率密度的计算公式.研究结果标明,逃逸几率密度与探测平面上逃逸点的位置、粒子的动量、初始出射角及与微腔的碰撞次数有关.为了更清楚的看出量子力学和经典力学之间的联系,我们对体系的半经典波函数进行傅里叶变换,给出了粒子的路径长度谱.路径长度谱的每个峰值对应于一条粒子逃逸轨迹的长度.本文的研究对理解量子力学和经典力学之间的联系以及研究粒子在微腔中的的逃逸和输运过程有一定的参考价值.     

Fractional trajectories: Decorrelation versus friction

The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. We apply the general theory developed herein to the Lotka–Volterra ecological model, providing new insight into the final equilibrium state. The relaxation time to achieve this state is also considered.     

一个强、弱耗散功能可分隔系统中的特征激变

报道一个由保守映象和耗散映象不连续、不可逆地分段描述的系统，以及在其中发生的一例特征激变.激变的独特之处在于逃逸孔洞.由映象的不连续、不可逆性而导致相平面中出现一个胖分形迭代禁区网，它使得一个混沌吸引子突然失稳而发生激变后出现的两个周期吸引子的吸引域边界成为点滴状.仅仅在每个周期点邻近存在这样的一个作为逃逸孔洞的、受到强耗散性支配和禁区边界限制的规则边界吸引域. 关键词： 激变 保守映象 耗散映象 逃逸孔洞     

Isentropic equation of state of two-flavour QCD in a quasi-particle model

We examine the isentropic QCD equation of state within a quasi-particle model being adjusted to first principle QCD calculations of two quark flavours. In particular, we compare with Taylor expansion coefficients of energy and entropy densities and with the isentropic trajectories describing the hydrodynamical expansion of a heavy-ion collision fireball.     

Quantum mechanics in theK-field formalism: Kepler's problem for spin particles

Using the well-known Kepler's problem, an attempt is made to demonstrate a procedure for constructing a nonrelativistic approximation of a quantum-mechanical model for steady states of hydrogen atoms in the K-field formalism. In this model, an electron is assumed to possess an intrinsic moment (spin) which, according to Frenkel, is comparable to the magnetic moment. It is shown that Lyapunov-stable trajectories of the K-particle (a test point particle representing the classical model of an electron in an atom) correspond to the conventional steady states of hydrogen atoms, with the trajectories being similar to those in the spin-zero particle model. The proposed model of the electronic structure in a hydrogen atom provides an insight into the physical cause of the atomic superfine structure and the physical meaning of the constant α=c/mc. Tomsk Polytechnical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 50–54, October, 1999.     

Return maps of folded nodes and folded saddle-nodes

Folded nodes occur in generic slow-fast dynamical systems with two slow variables. Open regions of initial conditions flow into a folded node in an open set of such systems, so folded nodes are an important feature of generic slow-fast systems. Twisting and linking of trajectories in the vicinity of a folded node have been studied previously, but their consequences for global dynamical behavior have hardly been investigated. One manifestation of the twisting is as "mixed mode oscillations" observed in chemical and neural systems. This paper presents the first systematic numerical study of return maps for trajectories that flow through a region with a folded node. These return maps are approximated by rank-1 maps, and the local twisting of trajectories near a folded node gives rise to multiple turning points in the approximating one dimensional maps. A variant of the forced van der Pol system is used here to illustrate that folded nodes can be a "chaos-generating" mechanism. Folded saddle-nodes occur in generic one-parameter families of slow-fast dynamical systems with two slow variables. These bifurcations give birth to folded nodes. Numerical simulations demonstrate that return maps of systems that are close to a folded saddle-node can be even more complex than those of folded nodes that are far from folded saddles.