Related papers: Algorithmic Chaos
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
Quantum Chaos has originally emerged as the field which studies how the properties of classical chaotic systems arise in their quantum counterparts. The growing interest in quantum many-body systems, with no obvious classical meaning has…
Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where 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,…
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…
We discuss the presence of both dynamical chaos and signals of a second--order phase transition in numerical Vlasov simulations of nuclear multifragmentation. We find that chaoticity and criticality are strongly related and play a crucial…
This is the contribution to Quarks'2018 conference proceedings. This contribution is devoted to the holographic description of chaos and quantum complexity in the strongly interacting systems out of equilibrium. In the first part of the…
We propose an uncertainty principle for chaos, focusing on two key characteristics: alpha unpredictability and Lorenz sensitivity. This principle outlines a limitation on the relationship between two infinite sequences that underpin these…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
Chaos degree defined through two complexities in information dynamics is applied to some deterministic dynamical models. It is shown that this degree well describes the chaostic feature of the models.
In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity…
Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude…
A novel topological and computational method for 'motion' is described. Motion is constrained by inequalities in terms of Kolmogorov Complexity. Causality is obtained as the output of a high-pass filter, passing through only high values of…
We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…