相关论文: Stochastic ionization through noble tori: Renormal…

A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity…

In this article, we describe a new renormalization-group scheme for analyzing the breakup of invariant tori for Hamiltonian systems with two degrees of freedom. The transformation, which acts on Hamiltonians that are quadratic in the action…

We consider a toy model for emergence of chaos in a quantum many-body short-range-interacting system: two one-dimensional hard-core particles in a box, with a small mass defect as a perturbation over an integrable system, the latter…

We analyze on a simple classical billiard system the onset of chaotical behaviour in different dynamical states. A classical version of the "nuclear billiard" with a 2D deep Woods-Saxon potential is used. We take into account the coupling…

We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…

It has recently been speculated that statistical properties of chaos may be captured by weighted sums over unstable invariant tori embedded in the chaotic attractor of hyperchaotic dissipative systems; analogous to sums over periodic orbits…

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local…

How classical chaos emerges from the underlying quantum world is a fundamental problem in physics. The origin of this question is in the correspondence principle. Classical chaos arises due to non-linear dynamics, whereas quantum mechanics,…

We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…

We review recent progress in applying information- and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for…

Since the seminal work of Wiener, the chaos expansion has evolved to a powerful methodology for studying a broad range of stochastic differential equations. Yet its complexity for systems subject to the white noise remains significant. The…

Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one…

This study examines second-order dynamical systems incorporating Tikhonov regularization. It focuses on how nonlinearities induce bifurcations and chaotic dynamics. By using Lyapunov functions, bifurcation theory, and numerical simulations,…

We describe a renormalization group transformation that is related to the breakup of golden invariant tori in Hamiltonian systems with two degrees of freedom. This transformation applies to a large class of Hamiltonians, is conceptually…

In this article we study a relatively novel way of constructing chaotic sequences of probability measures supported on Kac's sphere, which are obtained as the law of a vector of $N$ i.i.d. variables after it is rescaled to have unit average…

What is chaos? Despite several decades of research on this ubiquitous and fundamental phenomenon there is yet no agreed-upon answer to this question. Recently, it was realized that all stochastic and deterministic differential equations,…

Quantum tunneling in the presence of chaos is analyzed, focusing especially on the interplay between quantum tunneling and dynamical localization. We observed flooding of potentially existing tunneling amplitude by adding noise to the…

To overcome topological constraints and improve the expressiveness of normalizing flow architectures, Wu, K\"ohler and No\'e introduced stochastic normalizing flows which combine deterministic, learnable flow transformations with stochastic…

We show analytically that Newtonian iterations, when applied to a polynomial equation, have a positive topological entropy. In a specific example of an attempt to ``find'' the real solutions of the equation $x^2+1=0$, we show that the…

Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…