Related papers: Yang-Mills Classical and Quantum Mechanics and Max…
The maximally chaotic K-systems are dynamical systems which have nonzero Kolmogorov entropy. On the other hand, the hyperbolic dynamical systems that fulfil the Anosov C-condition have exponential instability of phase trajectories, mixing…
We give a general review on the application of Ergodic theory to the investigation of dynamics of the Yang-Mills gauge fields and of the gravitational systems, as well as its application in the Monte Carlo method and fluid dynamics. In…
We are developing further our earlier suggestion to use hyperbolic Anosov C-systems for the Monte-Carlo simulations in high energy particle physics. The hyperbolic dynamical systems have homogeneous instability of all trajectories and as…
We analyse the infinite-dimensional limit of the maximally chaotic dynamical systems that are defined on N-dimensional tori. These hyperbolic systems found successful application in computer algorithms that generate high-quality…
We analyze how quantum mechanics reinstates confinement in Hamiltonian systems that are classically unstable and exhibit chaotic dynamics. Specifically, we consider two paradigmatic models: the Contopoulos Hamiltonian, an isotropic…
Yang-Mills fields are an important part of the non-Abelian space theory describing the properties of quark-gluon plasma. The dynamics of the classical fields are given by the Hamiltonian equations of motion, which contain the member of the…
We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive…
We study the quantization of two examples of classically chaotic dynamics, the Anosov dynamics of "cat maps" on a two dimensional torus, and the dynamics of baker's maps. Each of these dynamics is implemented as a discrete group of…
I describe the footprints of the classical chaos of the Yang-Mills fields in the quantum description. I also review the behavior of the BKL chaotic approach to the classical singularity on the basis of the Loop Quantum Gravity.
The uniformly hyperbolic Anosov C-systems defined on a torus have exponential instability of their trajectories, and as such C-systems have mixing of all orders and nonzero Kolmogorov entropy. The mixing property of all orders means that…
It is generally believed that the dynamics of simple fluids can be considered to be chaotic, at least to the extent that they can be modeled as classical systems of particles interacting with short range, repulsive forces. Here we give a…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
We study the classical non-linear dynamics of the $SU(2)$ Yang-Mills matrix model introduced in [1] as a low-energy approximation to two-color QCD. Restricting to the spin-0 sector of the model, we unearth an unexpected tetrahedral…
We have identified ultra-cold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement…
We present a comparative study of the dynamical behaviour of topological systems of recent interest, namely the non-Abelian Chern-Simons Higgs system and the Yang-Mills Chern-Simons Higgs system. By reducing the full field theories to…
The quantum chaos in the finite-temperature Yang-Mills-Higgs system is studied. The energy spectrum of a spatially homogeneous SU(2) Yang-Mills-Higgs is calculated within thermofield dynamics. Level statistics of the spectra is studied by…
We study the effects of addition of Chern-Simons (CS) term in the minimal Yang Mills (YM) matrix model composed of two $2 \times 2$ matrices with $SU(2)$ gauge and $SO(2)$ global symmetry. We obtain the Hamiltonian of this system in…
This paper studies the Yang--Mills ASD equation over the cylinder as a non-linear evolution equation. We consider a dynamical system consisting of bounded orbits of this evolution equation. This system contains many chaotic orbits, and…
This talk describes the evolution of studies of chaos in Yang-Mills fields, gravity, and cosmology. The main subject is a BKL regime near the singularity $t=0$ and its survival in higher dimensions and in string theory. We also describe the…
The Kolmogorov-Sinai (K-S) entropy is a central measure of complexity and chaos. Its calculation for many-body systems is an interesting and important challenge. In this paper, the evaluation is formulated by considering $N$-dimensional…