Level statistics for the even-even Yb isotopes

The level statistics of the even-even Yb isotopes are studied by using the energy levels calculated by the projected shell model. The spectrum of intrinsic states and band energies are also studied to discuss the generation of chaoticity. The energy dependence of the chaoticity is investigated, and a chaos to order transition is found.     

Broken Ergodicity in Classically Chaotic Spin Systems

A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties such as ergodicity and chaoticity are very different. Indeed, even in the presence of chaoticity, the model displays a lack of ergodicity only in presence of all to all interaction and below an energy threshold, that persists in the thermodynamical limit. The energy threshold can be found analytically and results can be generalized for a generic XY model with asymmetric coupling.     

IBFM for Ba isotopes and chaoticity

Fluctuation properties have been analysed for the energy levels predicted by IBFM calculations in the Ba isotopes¹²¹Ba to¹³¹Ba. The results indicate, in general, a situation which is close to the chaotic limit. For the lighter isotopes studied (121 and 123), a phase transition is obtained in the low-spin, positive parity states, from a situation close to regularity at low excitation energies, towards chaoticity at higher excitations.     

粒子-转子模型和推转壳模型中的能谱统计分析

用粒子–转子模型和推转壳模型研究了6个粒子分别填充在单j壳和双j壳上的混沌行为.分析了单j壳和双j壳情况下能谱的最近邻能级间距分布和谱刚度随自旋及推转频率的变化,结果表明,当组态空间大小不变时,系统在双j壳(g_7/2+d_5/2)情况下比在单j壳(i_13/2)情况下更规则,而当组态空间从单j壳(i_13/2)扩大到双j壳(i_13/2+g_9/2)时,系统的混沌程度变化不大.同时比较了将6个粒子的两体相互作用分别取为δ力和对力时的系统的混沌行为     

Chaotic sources and percolation of strings in heavy ion collisions

The chaoticity parameter of Bose–Einstein correlations is studied as a tool for analyzing the interaction between color strings in multiparticle production at high energies. Different scenarios of this interaction lead to a different behavior of with energy and atomic number of the participants. Comparison to the present experimental data favors the percolation of strings scenario. The one of its versions in which shows a peculiar dependence on the string density, very similar to the dependence of the fractional average cluster size, looks particularly attractive. Received: 19 February 2001 / Revised version: 5 July 2001 / Published online: 10 August 2001     

Energy Level Statistics in Particle—Rotor Model

Energy level statistics of a system consisting of six particles interacting by delta force in a two-j model coupled with a deformed core is studied in particle-rotor model.For single-j shell (i13/2) and two-j shell (g7/2 d5/2) the exact energies for our statistical analysis are obtained from a full diagonalization of the Hamiltonian,whilt in two-j case (i13/2 g9/2) the configuration truncation is used.The nearest-neighbor distribution of energy levels and spectral rigidity are studied as the function of spin.The results of single-j shell are compared with those in two-j case.It is showed that the system becomes more regular when single-j space (i13/2) is replaced by two-j shell (g7/2 d5/2) although the basis size of the configuration space is unchanged.The degree of chaoticity of the system,however,changes slightly when configuration space is enlarged by extending single-j shell (i13/2) to two-j shell (i13/2 g9/2).     

Hopf bifurcation and chaos in a single inertial neuron model with time delay

A delayed differential equation modelling a single neuron with inertial term subject to time delay is considered in this paper. Hopf bifurcation is studied by using the normal form theory of retarded functional differential equations. When adopting a nonmonotonic activation function, chaotic behavior is observed. Phase plots, waveform plots, and power spectra are presented to confirm the chaoticity.Received: 19 December 2003, Published online: 21 October 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Disorder in ballistic systems: A numerical analysis

We present a numerical analysis of the single particle energy spectra of ballistic condensed matter systems and compare with recent theoretical results. We show that the presence even of weak disorder induces full chaoticity on time scales larger than the elastic disorder scattering time. To disentangle the effect of boundary, respectively disorder scattering on the spectral statistics, different types of correlation functions are introduced and discussed.     

颗粒相干发射源的2π和3π玻色-爱因斯坦关联

在假设由同一颗粒发射的π介子为相干发射的条件下, 给出了颗粒发射源模型的2π及3π关联函数, 发射源的混沌性随颗粒数目的增加而增大. 此外, 对颗粒相干发射源及部分相干高斯源的归一化纯3π关联进行比较, 发现当2π关联的混沌性参量小于0.8时, 两种发射源的归一化纯3π关联值在小Q₃区域有明显差别.     

Pairing and spectral statistics of low energy levels

The interplay of pairing with the different terms of the residual interaction is explored for the low-lying energy levels of semi-magic nuclei from the point of view of spectral statistics. The reduced degree of chaoticity present in this nuclei is shown to be directly related to the strength of the pairing interaction with respect to the total residual interaction. On the contrary, the pairing strength does not influence the spectral statistics near the ground state for nuclei with both neutrons and protons outside closed shells.     

Bose-Einstein correlations of pion wavepackets

A wavepacket model for a system of free pions, which takes into account the full permutation symmetry of the wavefunction and which is suitable for any phase space parametrization is developed. The properties of the resulting mixed ensembles and the two-particle correlation function are discussed. A physical interpretation of the chaoticity λ as localization of the pions in the source is presented. Two techniques to generate test-particles, which satisfy the probability densities of the wavepacket state, are studied:

1. A Monte Carlo procedure in momentum space based on the standard Metropolis technique.
2. A molecular dynamic procedure using Bohm’s quantum theory of motion. In order to reduce the numerical complexity, the separation of the wavefunction into momentum space clusters is discussed. In this context the influence of an unauthorized factorization of the state, i. e. the omission of interference terms, is investigated. It is shown that the correlation radius remains almost uneffected, but the chaoticity parameter decreases substantially. A similar effect is observed in systems with high multiplicities, where the omission of higher order corrections in the analysis of two-particle correlations causes a reduction of the chaoticity and the radius. The approximative treatment of the Coulomb interaction between pions and the source is investigated. The results suggest that Coulomb effects on the correlation radii are not symmetric for pion pairs of different charges. For (π^?,π^?) pairs the radius, integrated over the whole momentum spectrum, increases substantially, while for (π⁺,π⁺) pairs the radius remains almost unchanged.

     

Control methods for problems of mixing and coherence in chaotic maps and flows

We review a variety of control methods which are capable of enhancing the chaoticity and mixing properties of chaotic flows and also methods which work towards promoting the coherence properties of such flows. We discuss a parameter control method which can enhance the chaoticity and the rate of mixing of dissipative as well as conservative flows and outline methods which promote global mixing by the addition of noise and by preventing island formation. As the inverse side of this problem, we summarize methods which can create coherent structures in chaotic dynamical flows. We also discuss the utility of these methods from the point of view of applications as well as for understanding phenomena which occur in natural systems.     

Chaotic electron trajectories in electromagnetic wiggler free-electron laser with a guide magnetic field

Summary The Hamiltonian for an electron travelling through a large-amplitude backward electromagnetic wave, an axial guide magnetic field and radiation field is formulated. Poincaré surface-of-section plots show that this Hamiltonian is non-integrable, and leads to chaotic trajectories. Equilibrium conditions are derived in the limit where the radiation field approaches zero. Compared to conventional FEL, the total energy of the system at pondermotive resonanceE _c is large, while the electron's critical energy γ_c is low for electromagnetic wiggler FEL. Moreover, the threshold wave amplitude (A _r=A _c) of beam chaoticity is found at lower values of the radiation field amplitude compared to magnetostatic wiggler FEL. Previous features confirmed that electromagnetic wiggler FEL can operate more coherently and more efficiently at moderated particle's energy compared to magnetostatic wiggler FEL.     

Jacobi fields on statistical manifolds of negative curvature

Two entropic dynamical models are considered. The geometric structure of the statistical manifolds underlying these models is studied. It is found that in both cases, the resulting metric manifolds are negatively curved. Moreover, the geodesics on each manifold are described by hyperbolic trajectories. A detailed analysis based on the Jacobi equation for geodesic spread is used to show that the hyperbolicity of the manifolds leads to chaotic exponential instability. A comparison between the two models leads to a relation among statistical curvature, stability of geodesics and relative entropy-like quantities. Finally, the Jacobi vector field intensity and the entropy-like quantity are suggested as possible indicators of chaoticity in the ED models due to their similarity to the conventional chaos indicators based on the Riemannian geometric approach and the Zurek-Paz criterion of linear entropy growth, respectively.     

The complexity of proving chaoticity and the Church-Turing thesis

Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.     

Finite-temperature Bose-Einstein distribution functions of identical particles

We study the evolution properties of propagating identical particles produced at a finite temperature in a randomly distributed environment. The lower bound on the spacetime size of the multiparticle production region and the correlation chaoticity are derived.     

Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei

Statistical properties of the realistic energy spectra of the odd-odd nuclei¹⁰⁶Ag,¹⁹⁸Au,¹³⁴Cs,⁴⁰K and⁹⁴Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of theΔ ₃ statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the transitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics. Communicated by X. Campi     

Regular nonlinear response of the driven Duffing oscillator to chaotic time series

Nonlinear response of the driven Duffng oscillator to periodic or quasi-periodic signals has been well studied.In this paper,we investigate the nonlinear response of the driven Duffng oscillator to non-periodic,more specifically,chaotic time series.Through numerical simulations,we find that the driven Duffng oscillator can also show regular nonlinear response to the chaotic time series with different degree of chaos as generated by the same chaotic series generating model,and there exists a relationship between the state of the driven Duffng oscillator and the chaoticity of the input signal of the driven Duffng oscillator.One real-world and two artificial chaotic time series are used to verify the new feature of Duffng oscillator.A potential application of the new feature of Duffng oscillator is also indicated.     

Level density fluctuations and characterization of chaos in the realistic model spectra for odd-odd nuclei

Statistical properties of the realistic energy spectra of the odd-odd nuclei ¹⁰⁶Ag, ¹⁹⁸Au, ¹³⁴Cs, ⁴⁰K and ⁹⁴Rb, calculated within the Interacting Boson Fermion Fermion Model, are investigated by means of the Δ₃ statistics and the Nearest Neighbor Spacing Distribution method. New probability distribution function, which describes well the calculated results and enables the characterization of chaos with a physically meaningfull parameter, is proposed. Level spacing fluctuations of the examined nuclei exhibit the transitional behavior between Poisson and GOE limits, revealing different degrees of chaoticity in their dynamics.     

弱相互作用玻色-爱因斯坦凝聚体中涡旋动力学与量子混沌轨道简

利用变分法和数值模拟方法,我们分别从解析上和数值上研究了弱相互作用玻色-爱因斯坦凝聚体中不同涡旋蔟的动力学性质.借助玻姆量子力学中的方法,我们定义了相应量子流体中的量子轨道,并且研究了由于不同涡旋结构的存在而导致量子轨道出现混沌的性质.当存在一单涡旋,我们发现混沌轨道出现与否和涡旋轨道的形状紧密相关.此外,玻色凝聚体原子中的两体相互作用对各向异性谐振子势下涡旋对出现时量子轨道混沌的发生也具有重要的作用.因为这一非线性相互作用会破坏相应速度场的时间周期性.最后,在涡旋极子情形下,我们还讨论了由于涡旋相互激发或淹没的作用而导致规则岛膨胀的性质.这些规则区域镶嵌在一定的混沌海中.