Multicanonical Sampling of Rare Trajectories in Chaotic Dynamical Systems

Probing rare physical trajectories with Lyapunov weighted dynamics

The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition, atypical structures like the first chaotic regions to appear, or the last regular islands to survive, play a crucial role in many physical situations. For instance, resonances and separatrices determine the fate of planetary systems, and localised objects like solitons and breathers provide mechanisms of energy transport in nonlinear systems such as Bose-Ein…

Rare events, exponential hitting times and extremal indices via spectral perturbation

We discuss how an eigenvalue perturbation formula for transfer operators of dynamical systems is related to exponential hitting time distributions and extreme value theory for processes generated by chaotic dynamical systems. We also list a number of piecewise expanding systems to which this general theory applies and discuss the prospects to apply this theory to some classes of piecewise hyperbolic systems.

弹跳球模型低能域中的稀有事件

Rare events for low energy domain in bouncing ball model

该研究针对弹跳球模型低能域混沌动力学，揭示多次碰撞概率分布遵循幂律且对控制参数具有标度不变性，涉及粒子与固定及周期性运动壁的弹性碰撞及二维映射描述。

利用机器学习技术预测混沌动力系统时间序列中极端事件的方法

Approach to predicting extreme events in time series of chaotic dynamical systems using machine learning techniques

提出用卷积神经网络分类混沌系统状态，在Hénon映射时间序列中预测极端事件，过渡状态预测成功率超80%。

混沌系统中动力学可观测量分布的显著相似性

Remarkable similarities in distributions of dynamical observables in chaotic systems

本研究针对混沌系统的动力学可观测量，发现不同函数构建的可观测量可共享相同速率函数，提出“导出型”函数解释该相似性，并验证了开映射位置可观测量、logistic映射FTLE均属此类，为相关已有结果提供了简洁解释。

Geometric dynamical observables in rare gas crystals

We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard mehods of classical statistical mechanics, i.e. Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard Jones crystal modeling solid Xen…

Exploring quantum chaos with a single nuclear spin

Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to their discrete spectrum. Nonetheless, the dynamics of quantum systems whose classical counterparts are chaotic are expected to show some features that resemble chaotic motion. Among the many controversial aspects of the quantum-classical boundary, the emergence of chaos remains among the least experimentally verified. Time-resolved observations of quantum chaot…

MLC电路中的极端事件

Extreme events in MLC circuit

研究揭示了MLC电路中极端事件的动态机制，通过力场和相空间分解解释了极端事件的产生，结合极值理论分析了其统计特性。

稀有事件采样用于移动目标：一般环流模型中温度和日降水量的极值

Rare event sampling for moving targets: extremes of temperature and daily precipitation in a general circulation model

本文提出TEAMS算法，通过适应性多级分裂方法加速极值估计，实现对地表温度和日降水量极值的快速评估，适用于复杂物理模型下的风险评估。

Thermodynamic formalism and localization in Lorentz gases and hopping models

The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $ψ(β)$. The inverse-temperature like variable $β$ allows one to scan the structure of the probability distribution in the dynamic phase space. This formalism is applied here to a Lorentz Lattice Gas, where a particle moving on a lattice of size $L^d$ collides with fixed scatterers placed at random locations. Here we give rigorous arguments that the Ruelle pressure in the limit of infinit e systems has two branches joining with a slope discontinuity at $β= 1$. The low and high $β$--bran…