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We investigate the dynamics of information scrambling in bosonic systems undergoing Gaussian unitary evolution associated with quadratic Hamiltonians. For initial Gaussian states, we observe the disappearance of the memory effect in the…
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 here describe the possibility of a synthetic description of the onset of Chaos in many degrees of freedom dynamical systems within the framework of the geometric description of dynamics. We show how this approach to instability helps to…
We present a Hamiltonian approach for the wellknown Eigen model of the Darwin selection dynamics. Hamiltonization is carried out by means of the embedding of the population variable space, describing behavior of the system, into the space…
The resolution of geometric frustration in systems with continuous degrees of freedom often involves a cooperative inhomogeneous response and super-extensive energy scaling. In contrast, the frustration in frustrated Ising-like spin systems…
It is well-known that the fundamental diagram in a realistic traffic system is featured by capacity drop. From a mesoscopic approach, we demonstrate that such a phenomenon is linked to the unique properties of stochastic noise, which, when…
The symmetric harmonic three-mass system with finite rest lengths, despite its apparent simplicity, displays a wide array of interesting dynamics for different energy values. At low energy the system shows regular behavior that produces a…
We propose a method to manipulate, possibly faster than adiabatically, four-level systems with time-dependent couplings and constant energy shifts (detunings in quantum-optical realizations). We inversely engineer the Hamiltonian, in…
Understanding how frustration and disorder shape relaxation in complex systems is a central problem in statistical physics and quantum annealing. Spin-glass models provide a natural framework to explore this connection, as their energy…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
The development of physical simulators, called Ising machines, that sample from low energy states of the Ising Hamiltonian has the potential to drastically transform our ability to understand and control complex systems. However, most of…
We propose a new driving scheme, when different parts of a system are driven with different, generally incommensurate, frequencies. Such driving provides a flexible handle to control various properties of the system and to obtain new types…
The Hamiltonian dynamics of the classical $\phi^4$ model on a two-dimensional square lattice is investigated by means of numerical simulations. The macroscopic observables are computed as time averages. The results clearly reveal the…
Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…
As a result of resonance overlap, planetary systems can exhibit chaotic motion. Planetary chaos has been studied extensively in the Hamiltonian framework, however, the presence of chaotic motion in systems where dissipative effects are…
A continuum model for self-organized dynamics is numerically investigated. The model describes systems of particles subject to alignment interaction and short-range repulsion. It consists of a non-conservative hyperbolic system for the…
Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3].…
Multistability is a common phenomenon which naturally occurs in complex networks. If coexisting attractors are numerous and their basins of attraction are complexly interwoven, the long-term response to a perturbation can be highly…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…