Determination of Domain of Attraction by Short-Time Overlap Dynamics in Neural Networks

Since the overlap dynamics of spin-glass-like neural network is solely governed by such two parameters, the symmetry of the net's connections and the stabilities of the embedded patterns, we propose that the domain of attraction of a network could be determined by a short-time (at least the first two-step) dynamics, in which both parameters begin to be visible.The first step overlap dynamics Q calculated by probability theory and the second step overlap dynamics for pseudo-inverse-model is obtained by extended Krauth's theory. The calculated domain of attraction for this model is in good agreement with the results obtained by computer simulation.     

Presentation functions,fixed points,and a theory of scaling function dynamics

Presentation functions provide the time-ordered points of the forward dynamics of a system as successive inverse images. They generally determine objects constructed on trees, regular or otherwise, and immediately determine a functional form of the transfer matrix of these systems. Presentation functions for regular binary trees determine the associated forward dynamics to be that of a period doubling fixed point. They are generally parametrized by the trajectory scaling function of the dynamics in a natural way. The requirement that the forward dynamics be smooth with a critical point determines a complete set of equations whose solution is the scaling function. These equations are compatible with a dynamics in the space of scalings which is conjectured, with numerical and intuitive support, to possess its solution as a unique, globally attracting fixed point. It is argued that such dynamics is to be sought as a program for the solution of chaotic dynamics. In the course of the exposition new information pertaining to universal mode locking is presented.     

Nonequilibrium dynamics of ultracold Fermi superfluids

The aim of this mini review is to survey the literature on the study of nonequilibrium dynamics of Fermi superfluids in the BCS and BEC limits, both in the single channel and dual channel cases. The focus is on mean field approaches to the dynamics, with specific attention drawn to the dynamics of the Ginzburg-Landau order parameters of the Fermi and composite Bose fields, as well as on the microscopic dynamics of the quantum degrees of freedom. The two approaches are valid approximations in two different time scales of the ensuing dynamics. The system is presumed to evolve during and/or after a quantum quench in the parameter space. The quench can either be an impulse quench with virtually instantaneous variation, or a periodic variation between two values. The literature for the order parameter dynamics, described by the time-dependent Ginzburg-Landau equations, is reviewed, and the works of the author in this area highlighted. The mixed phase regime in the dual channel case is also considered, and the dual order parameter dynamics of Fermi-Bose mixtures reviewed. Finally, the nonequilibrium dynamics of the microscopic degrees of freedom for the superfluid is reviewed for the self-consistent and non self-consistent cases. The dynamics of the former can be described by the Bogoliubov de-Gennes equations with the equilibrium BCS gap equation continued in time and self -consistently coupled to the BdG dynamics. The latter is a reduced BCS problem and can be mapped onto the dynamics of Ising and Kitaev models. This article reviews the dynamics of both impulse quenches in the Feshbach detuning, as well as periodic quenches in the chemical potential, and highlights the author’s contributions in this area of research.     

Modal Dynamics for Positive Operator Measures

The modal interpretation of quantum mechanics allows one to keep the standard classical definition of realism intact. That is, variables have a definite status for all time and a measurement only tells us which value it had. However, at present modal dynamics are only applicable to situations that are described in the orthodox theory by projective measures. In this paper we extend modal dynamics to include positive operator measures (POMs). That is, for example, rather than using a complete set of orthogonal projectors, we can use an overcomplete set of nonorthogonal projectors. We derive the conditions under which Bell's stochastic modal dynamics for projective measures reduce to deterministic dynamics, showing (incidentally) that Brown and Hiley's generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus derived. We then show how deterministic dynamics for positive operators can also be derived. As a simple case, we consider a Harmonic oscillator, and the overcomplete set of coherent state projectors (i.e., the Husimi POM). We show that the modal dynamics for this POM in the classical limit correspond to the classical dynamics, even for the nonclassical number state |n>. This is in contrast to the Bohmian dynamics, which for energy eigenstates, the dynamics are always non-classical.     

Can potentially useful dynamics to solve complex problems emerge from constrained chaos and/or chaotic itinerancy?

Complex dynamics including chaos in systems with large but finite degrees of freedom are considered from the viewpoint that they would play important roles in complex functioning and controlling of biological systems including the brain, also in complex structure formations in nature. As an example of them, the computer experiments of complex dynamics occurring in a recurrent neural network model are shown. Instabilities, itinerancies, or localization in state space are investigated by means of numerical analysis, for instance by calculating correlation functions between neurons, basin visiting measures of chaotic dynamics, etc. As an example of functional experiments with use of such complex dynamics, we show the results of executing a memory search task which is set in a typical ill-posed context. We call such useful dynamics "constrained chaos," which might be called "chaotic itinerancy" as well. These results indicate that constrained chaos could be potentially useful in complex functioning and controlling for systems with large but finite degrees of freedom typically observed in biological systems and may be such that working in a delicate balance between converging dynamics and diverging dynamics in high dimensional state space depending on given situation, environment and context to be controlled or to be processed.     

超冷费米气体的膨胀动力学研究新进展

多体系统的非平衡动力学演化是当前物理学中最具挑战性的问题之一.超冷量子费米原子气体具有较强的可控性,是研究多体非平衡动力学的理想系统,可以用来模拟和理解大爆炸后的早期宇宙、重离子碰撞中产生的夸克-胶子以及核物理等动力学.一般多体系统演化是非常复杂的,往往需要利用对称性来研究.利用Feshbach共振可以制备标度不变的费米原子气体:无相互作用和幺正费米量子气体.当远离平衡态时,可利用普适的指数和函数来刻画,其动力学可以通过对系统的时空演化进行标度变换来识别.本文主要介绍近年来强相互作用超冷费米气体的膨胀动力学研究进展,包括原子气体的各向异性展开、标度动力学和Efimovian膨胀动力学.     

Scaling laws and memory effects in the dynamics of liquids and proteins

Recent progress in the numerical calculation of memory functions from molecular dynamics simulations allowed the gaining of deeper insight into the relaxation dynamics of liquids and proteins. The concept of memory functions goes back to the work of R. Zwanzig on the generalized Langevin equation, and it was the basis for the development of various dynamical models for liquids. In this article we present briefly a method for the numerical calculation of memory functions, which is then applied to study their scaling behavior in normal and fractional Brownian dynamics. It has been shown recently that the model of fractional Brownian dynamics constitutes effectively a link between protein dynamics on the nanosecond time scale, which is accessible to molecular dynamics simulations and thermal neutron scattering, and the much longer time scale of functional protein dynamics, which can be studied by fluorescence correlation spectroscopy. The text was submitted by the authors in English. Affiliated with the University of Orléans.     

Chaos in intrinsic motion of nuclei and its role in dissipative collective dynamics

We shall discuss the role of chaotic intrinsic motion in dissipative dynamics of the collective coordinates for nuclear systems. Using the formalism of linear response theory, it will be shown that the dissipation in adiabatic collective motion depends on the degree of chaos in the intrinsic dynamics of a system. This gives rise to a shape dependent dissipation rate for collective coordinates when the intrinsic motion is described by the independent particle model in a nucleus. The shape dependent chaos parameter measuring the degree of chaos in the intrinsic dynamics of the nuclear system will be obtained using the interpolating Brody distribution of nearest neighbour spacings in the single particle energy spectrum. A similar shape dependence is also found to be essential for phenomenological dissipation rates used in fission dynamics calculations.     

A Remark on the Mean-Field Dynamics of Many-Body Bosonic Systems with Random Interactions and in a Random Potential

The mean-field limit for the dynamics of bosons with random two-body interactions and in the presence of a random external potential is rigorously studied, both for the Hartree dynamics and the Gross–Pitaevskii dynamics. First, it is shown that, for interactions and potentials that are almost surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a single particle nonlinear evolution that is described by the Hartree equation. This is an Egorov-type theorem for many-body quantum systems with random interactions. The analysis is then extended to derive the Gross–Pitaevskii equation with random interactions.     

Newtonian Kinetic Theory and the Ergodic-Nonergodic Transition

In a recent work we have discussed how kinetic theory, the statistics of classical particles obeying Newtonian dynamics, can be formulated as a field theory. The field theory can be organized to produce a self-consistent perturbation theory expansion in an effective interaction potential. In the present work we use this development for investigating ergodic-nonergodic (ENE) transitions in dense fluids. The theory is developed in terms of a core problem spanned by the variables ρ, the number density, and B, a response density. We set up the perturbation theory expansion for studying the self-consistent model which gives rise to a ENE transition. Our main result is that the low-frequency dynamics near the ENE transition is the same for Smoluchowski and Newtonian dynamics. This is true despite the fact that term by term in a density expansion the results for the two dynamics are fundamentally different.     

Symmetry-adapted graph neural networks for constructing molecular dynamics force fields

Molecular dynamics is a powerful simulation tool to explore material properties. Most realistic material systems are too large to be simulated using first-principles molecular dynamics. Classical molecular dynamics has a lower computational cost but requires accurate force fields to achieve chemical accuracy. In this work, we develop a symmetry-adapted graph neural network framework called the molecular dynamics graph neural network(MDGNN) to construct force fields automatically for molecular dynamics simulations for both molecules and crystals. This architecture consistently preserves translation, rotation, and permutation invariance in the simulations. We also propose a new feature engineering method that includes high-order terms of interatomic distances and demonstrate that the MDGNN accurately reproduces the results of both classical and first-principles molecular dynamics. In addition, we demonstrate that force fields constructed by the proposed model have good transferability.The MDGNN is thus an efficient and promising option for performing molecular dynamics simulations of large-scale systems with high accuracy.     

Active nonlinear microrheology in a glass-forming Yukawa fluid

A molecular dynamics computer simulation of a glass-forming Yukawa mixture is used to study the anisotropic dynamics of a single particle pulled by a constant force. Beyond linear response, a scaling regime is found where a force-temperature superposition principle of a Peclet number holds. In the latter regime, the diffusion dynamics perpendicular to the force can be mapped on the equilibrium dynamics in terms of an effective temperature, whereas parallel to the force a superdiffusive behavior is seen in the long-time limit. This behavior is associated with a hopping motion from cage to cage and can be qualitatively understood by a simple trap model.     

Globally enumerating unstable periodic orbits for observed data using symbolic dynamics

The unstable periodic orbits of a chaotic system provide an important skeleton of the dynamics in a chaotic system, but they can be difficult to find from an observed time series. We present a global method for finding periodic orbits based on their symbolic dynamics, which is made possible by several recent methods to find good partitions for symbolic dynamics from observed time series. The symbolic dynamics are approximated by a Markov chain estimated from the sequence using information-theoretical concepts. The chain has a probabilistic graph representation, and the cycles of the graph may be exhaustively enumerated with a classical deterministic algorithm, providing a global, comprehensive list of symbolic names for its periodic orbits. Once the symbolic codes of the periodic orbits are found, the partition is used to localize the orbits back in the original state space. Using the periodic orbits found, we can estimate several quantities of the attractor such as the Lyapunov exponent and topological entropy.     

Nonlinear dynamics extraction for time-delay systems using modular neural networks synchronization and prediction

It is shown that the nonlinear dynamics of chaotic time-delay systems can be reconstructed using a new type of neural network with two modules: one for nonfeedback part with input data delayed by the embedding time, and a second one for the feedback part with input data delayed by the feedback time. The method is applied to both simulated and experimental data from an electronic analog circuit of the Mackey–Glass system. Better results are obtained for the modular than for feedforward neural networks for the same number of parameters. It is found that the complexity of the neural network model required to reconstruct nonlinear dynamics does not increase with the delay time. Synchronization between the data and the model with diffusive coupling is also achieved. We have also shown by iterating the model from the present point that the dynamics can be predicted with a forecast horizon larger than the feedback delay time.     

Free electron laser spectral dynamics with a modulation of electron beam energy

Recent experimental and theoretical works on free electron laser spectral dynamics have pointed out the difficulty to obtain a narrow and stable spectrum operation. This goal can only be achieved by avoiding the sideband generation leading to a broadband and unstable spectrum. Tapered wiggler and two-frequency wiggler are well suited for combining sharp spectrum and high efficiency but are not really compatible with a wide tunability of laser light. Filtering sidebands is a good way for lower power experiments but it seems to be difficult to conceive wideband filters, specially in the far-infrared region. Modulation of electron energy is a new potential soft way for controlling the spectral dynamics of longpulse free electron laser. Spectral dynamics under the modulation is investigated in the linear and non-linear regimes in the far-infrared region. Simulations show that a pulsed and sharp spectrum behavior can be obtained by optimizing the modulation parameters. The interest of such a method for the far-infrared experiments is discussed.     

Pancharatnam phase of two Cooper-pair boxes in a dissipative cavity

The time evolution of a single Cooper pair in the presence of another Cooper pair interacting with an electromagnetic field in a dissipative cavity is presented. The strong dependence of the dynamics of two superconducting charge qubits interacting with the microcavity field on the instantaneous phase shift experienced by the second qubit is demonstrated. The Pancharatnam phase is found to be more sensitive than the population dynamics to the phase shift. This leads us to suggest a new technique for controlling the system dynamics. Furthermore, although the atom is not directly coupled to the cavity modes, its coherent properties are found to be strongly influenced by dissipation, both qualitatively and quantitatively.     

并行化光滑分子动力学方法及其与分子动力学的耦合

提出光滑分子动力学方法(SMD)的并行化计算方法,编制光滑分子动力学以及光滑分子动力学-分子动力学(SMD-MD)耦合的并行程序,并分析铜纳米单晶的单向拉伸和带裂纹板的拉伸问题.光滑分子动力学在分子动力学基础上引入背景网格,在背景网格点上求解运动方程,由此将控制MD临界时间步长的因素化为背景网格单元尺寸,扩大可用的时间积分步长,缩短总计算时间.通过单晶拉伸和带裂纹板拉伸等较大规模问题的计算,验证方法的正确性.与传统分子动力学相比,SMD和SMD-MD耦合方法可以节约计算时间.     

Dynamics between order and chaos revisited

We show that dynamics between order and chaos, namely strange nonchaotic dynamics can be efficiently studied by means of recurrence properties. Different transitions to this dynamics in coupled R?ssler oscillators are revealed by some measures of complexity based on the recurrence time, which is the time needed for a system to recur to a former visited neighborhood. Furthermore, regions of the parameter space where the system is in non-phase, imperfect-phase or phase synchronization are depicted by means of recurrence based indices such as the generalized autocorrelation function and the correlation of probability of recurrence.     

Efficient formalism for large-scale ab initio molecular dynamics based on time-dependent density functional theory

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) simulations is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schr?dinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast with other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large-scale AIMD simulations.     

Network evolution driven by dynamics applied to graph coloring

An evolutionary network driven by dynamics is studied and applied to the graph coloring problem. From an initial structure, both the topology and the coupling weights evolve according to the dynamics. On the other hand, the dynamics of the network are determined by the topology and the coupling weights, so an interesting structure-dynamics co-evolutionary scheme appears. By providing two evolutionary strategies, a network described by the complement of a graph will evolve into several clusters of nodes according to their dynamics. The nodes in each cluster can be assigned the same color and nodes in different clusters assigned different colors. In this way, a co-evolution phenomenon is applied to the graph coloring problem. The proposed scheme is tested on several benchmark graphs for graph coloring.