Related papers: Kac's chaos and Kac's program
In this paper, we first investigate the well-posedness of a backward stochastic differential equation where the driver depends on the law of the solution conditioned to a common noise. Under standard assumptions, we show that existence and…
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…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…
In this work, we generalize M. Kac's original many-particle binary stochastic model to derive a space homogeneous Boltzmann equation that includes a linear combination of higher-order collisional terms. First, we prove an abstract theorem…
We consider a $N$-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit $N \to \infty$, as following from the previous…
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…
In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now named by the more fashionable term of deterministic…
We present a method to obtain sharp local propagation of chaos results for a system of N particles with a diffusion coefficient that it not constant and may depend of the empirical measure. This extends the recent works of Lacker [14] and…
A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy,…
We study the derivative-free global optimization algorithm Consensus-Based Optimization (CBO), establishing uniform-in-time propagation of chaos as well as an almost uniform-in-time stability result for the microscopic particle system.…
We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system.…
We obtain quantitative estimates on quenched propagation of chaos for Langevin spin glass dynamics with i.i.d. disorder. Prior work in the case of Gaussian disorder established the qualitative convergence of the law of a single spin to a…
The Bird and Nanbu systems are particle systems used to approximate the solution of the mollied Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94, GM97, GM99], we use coupling techniques and…
Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting…
The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
We review recent developments encompassing the description of quantum chaos in holography. We discuss the characterization of quantum chaos based on the late time vanishing of out-of-time-order correlators and explain how this is realized…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
We establish a rigorous connection between quantum coherence and quantum chaos by employing coherence measures originating from the resource theory framework as a diagnostic tool for quantum chaos. We quantify this connection at two…