相关论文: Recurrence Time Statistics for Finite Size Interva…

We study numerically the evolution of energy-level statistics as an integrability-breaking term is added to the XXZ Hamiltonian. For finite-length chains, physical properties exhibit a cross-over from behavior resulting from the Poisson…

We investigate the predictive power of recurrent neural networks for oscillatory systems not only on the attractor, but in its vicinity as well. For this we consider systems perturbed by an external force. This allows us to not merely…

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…

The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral…

Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…

A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…

We present results on dynamical processes that exhibit a stretched exponential relaxation. When the relaxation is a result of two competing exponential processes, the size of the system, although macroscopic, play a dominant role. There…

The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence…

We derive a general formalism with which it is possible to obtain the time dependence of the echo size for a spin in a stochastic field environment. Our model is based on ``strong collisions''. We examine in detail three cases where: (I)…

The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced…

We consider continuous space-time decay-surge population models which are semi- stochastic processes for which deterministically declining populations, bound to fade away, are rein- vigorated at random times by bursts or surges of random…

We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…

We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…

The influence of periodic boundary conditions (implicit finite-size effects) on the anisotropy of pair correlations in computer simulations is studied for a dense classical fluid of pair-wise interacting krypton atoms near the triple point.…

As has long been known to computer scientists, the performance of probabilistic algorithms characterized by relatively large runtime fluctuations can be improved by applying a restart, i.e., episodic interruption of a randomized…

We quantify the finite size effects in a stochastic network made up of rate neurons, for several kinds of recurrent connectivity matrices. This analysis is performed by means of a perturbative expansion of the neural equations, where the…

We study the statistics of the recurrence times between earthquakes above a certain magnitude M$ in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time $\tau_0$. As a…

The Battle of the Sexes describes asymmetric conflicts in mating behavior of males and females. Males can be philanderer or faithful, while females are either fast or coy, leading to a cyclic dynamics. The adjusted replicator equation…

We investigate the recurrence properties of the time series of quantum mechanical expectation values, in terms of two representative models for a single-mode radiation field interacting with a nonlinear medium. From recurrence-time…