Related papers: Time-delay, energy-continuum, and systematics of p…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
We study both analytically and numerically how the electronic structure and the transport properties of a two-dimensional disordered system are modified in the presence of resonances. The energy dependence of the density of states and the…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
Motivated by evidence for the existence of dark matter, many new physics models predict the pair production of new particles, followed by the decays into two invisible particles, leading to a momentum imbalance in the visible system. For…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…
The planetary dynamics of $4/3$, $3/2$, $5/2$, $3/1$ and $4/1$ mean motion resonances is studied by using the model of the general three body problem in a rotating frame and by determining families of periodic orbits for each resonance.…
Random non-reciprocal interactions between a large number of conserved densities are shown to enhance the stability of the system towards pattern formation. The enhanced stability is an exact result when the number of species approaches…
We follow the time sequence of binary elastic collisions in a small collection of hard-core particles. Intervals between the collisions are characterized by the numbers of collisions of different pairs in a given time. It was shown…
Resonance, defined as the oscillation of a system when the temporal frequency of an external stimulus matches a natural frequency of the system, is important in both fundamental physics and applied disciplines. However, the spatial…
We show the relation between the Heisenberg averaging of regularized 2-point out-of-time ordered correlation function and the 2-point spectral form factor in bosonic quantum mechanics. The generalization to all even-point is also discussed.…
We review Bohr's reasoning in the Bohr-Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this…
The dynamical stability of tightly packed exoplanetary systems remains poorly understood. While for a two-planet system a sharp stability boundary exists, numerical simulations of three and more planet systems show that they can experience…
We have recently established a new method for measuring the mass of unstable particles produced at hadron colliders based on the analysis of the energy distribution of a massless product from their two-body decays. The central ingredient of…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
Resonances, or scattering poles, are complex numbers which mathematically describe meta-stable states: the real part of a resonance gives the rest energy, and its imaginary part, the rate of decay of a meta-stable state. This description…
We compare a number of methods used to locate resonances. These include the speed plot, the time-delay method of Eisenbud and Wigner, the time-delay matrix of Smith, and a modification by Ohmura. Numerical results show a consistency not…
TESS and Kepler have revealed that practically all close-in sub-Neptunes form in mean-motion resonant chains, most of which unravel on timescales of 100 Myr. Using N-body integrations, we study how planetary collisions from destabilized…
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the…