Related papers: Chaotic Symmetry Breaking and Dissipative Two-Fiel…
We discuss recent results obtained for the Hamiltonian Mean Field model. The model describes a system of N fully-coupled particles in one dimension and shows a second-order phase transition from a clustered phase to a homogeneous one when…
We investigate beyond-mean-field dynamics in a fully connected $\mathrm{SU}(3)$ spin-exchange model, focusing on the interplay between chaotic dynamics and quantum fluctuations. Using the two-particle irreducible (2PI) effective action…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
Parameter space of a driven damped oscillator in a double well potential presents either a chaotic trajectory with sign oscillating amplitude or a non-chaotic trajectory with a fixed sign amplitude. A network of such delay coupled damped…
Nonlinear dynamics of a bouncing ball moving in gravitational field and colliding with a moving limiter is considered. Displacement of the limiter is a quadratic function of time. Several dynamical modes, such as fixed points, 2 - cycles…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
We consider a permanent magnetic dipole in an oscillating magnetic field. This magnetic oscillator has two dynamical symmetries. With increasing the amplitude $A$ of the magnetic field, dynamical behaviors associated with the symmetries are…
In order to understand the parameters of the standard model of electroweak and strong interactions (coupling constants, masses, mixing angles) one needs to embed the standard model into some larger theory that accounts for the observed…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
We consider stochastically quantized self-interacting scalar fields as suitable models to generate dark energy in the universe. Second quantization effects lead to new and unexpected phenomena is the self interaction strength is strong. The…
Analytical solutions to the chaotic and ergodic motion of a certain class of one-dimensional dissipative and discrete dynamical systems are derived. This allows us to obtain exact expressions for physical properties like the time…
We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron…
The dynamics of closed scalar field FRW cosmological models is studied for several types of exponentially and more than exponentially steep potentials. The parameters of scalar field potentials which allow a chaotic behaviour are found from…
This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is…
We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry…
We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of…
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…
Dynamics of spontaneous symmetry breaking and fluctuations in the Lipkin-Meshkov-Glick model are investigated in a stochastic mean-field approach. Different from the standard mean-field, in the stochastic approach, initial state…