相关论文: On Kac's Chaos And Related Problems

The aim of this note is to revisit propagation of chaos for a Langevin-type interacting particle system used for sampling probability measures. The interacting particle system we consider coincides, in the setting of a log-quadratic target…

The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…

In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve…

The problem of determining the intrinsic quality of a signal processing system with respect to the inference of an unknown deterministic parameter $\theta$ is considered. While the Fisher information measure $F(\theta)$ forms a classical…

Two classically equivalent expressions of mutual information of probability distributions (classical bipartite states) diverge when extended to quantum systems, and this difference has been employed to define quantum discord, a quantifier…

Developing measures of quantum ergodicity and chaos stands as a foundational task in the study of quantum many-body systems. In this work, we propose metrics for these effects based on Hamiltonian learning that unify multiple advantages of…

A source of unpredictability is equivalent to a source of information: unpredictability means not knowing which of a set of alternatives is the actual one; determining the actual alternative yields information. The degree of…

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the…

Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system…

We study the time-evolution of cumulants of velocities and kinetic energies in the stochastic Kac model for velocity exchange of $N$ particles, with the aim of quantifying how fast these degrees of freedom become chaotic in a time scale in…

We study the coupled translational, electronic, and field dynamics of the combined system "a two-level atom + a single-mode quantized field + a standing-wave ideal cavity". We derive Hamilton -- Schr\"odinger equations for probability…

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our…

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the…

Uncertainty in the initial conditions of dynamical systems can cause exponentially fast divergence of trajectories, a signature of deterministic chaos. Here, we derive a classical uncertainty relation that sets a speed limit on the rates of…

Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We…

The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…

Quantum chaos is a quantum many-body phenomenon that is associated with a number of intricate properties, such as level repulsion in energy spectra or distinct scalings of out-of-time ordered correlation functions. In this work, we…

The notion of Bohr chaos was introduced in [3, 4]. We answer a question raised in [3] of whether a non uniquely ergodic minimal system of positive topological entropy can be Bohr chaotic. We also prove that all systems with the…

We show that the most important measures of quantum chaos like frame potentials, scrambling, Loschmidt echo, and out-of-time-order correlators (OTOCs) can be described by the unified framework of the isospectral twirling, namely the Haar…

We propose a new approach to define chaos in dynamical systems from the point of view of Information Dynamics. Observation of chaos in reality depends upon how to observe it, for instance, how to take the scale in space and time. Therefore…